One car travels due east at and a second car travels north s) .ngvtnkx+hsio 31-+0w ud11 mto)pmy nq7gat Are their velocities eq n11n3dt-+. hq mmugo7+pn)xktg) vios0 1wysual? Explain.

Can you give several examples of an object’s motion in which a gre k w s6naz(2hht+e,fr-t4tmf1at distance is traveled but the dhft fw, t 1mk4t ah6s+zer-n(2isplacement is zero?

Can the displacement vector for a particle moving iu0 :5okt ;ipi2n:gcacn two dimensions ever be longer than the length of path traveled by the particle over the same time intervalpa:nu:20c;tic5 igk o? Can it ever be less? Discuss.

$\text { If } \overrightarrow{\mathbf{V}}=\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{v}}_{2} \text {, is } V \text { necessarily greater than } V_{1} \text { and/or } V_{2} \text { ? Discuss. }$

  Two vectors have lengtho +w d /:.hb(+k+mcjvo/gjt bo $ V_{1}=3.5 \mathrm{~km} $ and $ V_{2}=4.0 \mathrm{~km}$ . What are the maximum and minimum magnitudes of their vector sum?max =    min =   

Can two vectors of unequal magnitude add up to ,.qbc f wb-3pb1oo;5brma noj9vw t-1give the zero vector? Can three unequal vectors? Uf5p o vo3- b.tabwcr -w9o;b11 ,mjbnqnder what conditions?

Can the magnitude of a vector ever (a) be equal to one of its componen7uc9 4lj01k u*:k qaf ofz 07kzmy3bgrts, or (b) be l*k 7u3qjr4zf7gf0b m:c kk youz01 a9less than one of its components?

  Can a particle with constant speed be accelerating? ----待选择----YesNo  What if it has constant velocity? ----待选择----YesNo 

At some amusement parks, to get on a moving “car” the riders vr1pjq1hy+ )av,) wkbfirst hop onto a moving walkway and then onto the cars themselves. )v ba ,1vpwr+ 1hykq)jWhy is this done?

If you are riding on a train that speeds past another train moving in th:h2( q11fs l5tlcxhkr8; w bpre same direction onhw rr1l5lkfh:b8s;c 2xp (tq1 an adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under an um besmc h:(.h0d:8otl6z ty sce+ro/,ebrella in a rainstorm where the drops fall vertically, you remars+tezs8o l cb.dct(6e/:hmoe ,y: 0hin relatively dry. However, if you start running, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at constant velocity, throws a( cr17:o1or a hro.tk8kdb c8o ball straight up into the air in her refehro78bca 8k:(tod c1.oo1 krrrence frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row at the same speed in still water, set off across4l nvfrefc.uj 99l- (v a river at the same time. A heads straight ar (ufv .c nfv9l9ejl4-cross and is pulled downstream somewhat by the current. The B heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baseball player “judges” the flight of fj :xe;zfd 10na fly ball? Which equation in this nz; :1f0djxe fChapter becomes part of the player’s intuition?

In archery, should the arrow u*dp 4p-4yoe8bo g*5 owp kui5be aimed directly at the target? How should your angle of aim depend on b8 4p eouo*-yg4ou*w5 pkpi5dthe distance to the target?

  A projectile is launched at an ang4yodaj vt 4j:f ekd(2q+:ds;mle of $30^{\circ}$ to the horizontal with a speed of $ 30 \mathrm{~m} / \mathrm{s}$. How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch?   

  Two cannonballs, A and B , are fired from the ground with identical initial sns l,zu5enwjwe4f:x 4z- b62 ubgn+.h peeds, but wnj b +u5n4gw,:b 2-wx4u eshlzf nez6.ith $ \theta_{\mathrm{A}} $ larger than $ \theta_{\mathrm{B}} $
(a)Which cannonball reaches a higher elevation? ----待选择----AB 
(b) Which stays longer in the air?  ----待选择----AB 
(c) Which travels farther? If the angle of a is 40 $^{\circ}$ the angle of b is 30$^{\circ}$  ----待选择----AB 

A car is driven 215 km west and then 85 km southwda sduo9/ ib9j jef/z7t8 +)dbest. What is the displacement of the d9z78jubs9 di+d/ jfe/b)o tacar from the point of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blomwy*i) cxyimsft 1fy(/g z6k(v+8n 3dcks east, and 16 blocks south. What is its final displacement from the origin? Assume 6si3yf((n *+kfvtdm xy)ywz m g/i18cthe blocks are equal length.    blocks

$\text { Show that the vector labeled "incorrect" in Fig. 3-6c is actually the difference of the two vectors. Is it }\\
\overrightarrow{\mathbf{v}}_{2}-\overrightarrow{\mathbf{v}}_{1} \text {, or } \overrightarrow{\mathbf{v}}_{\mathbf{1}}-\overrightarrow{\mathbf{v}}_{\mathbf{2}} ?$

  $\text { If } V_{x}=6.80 \text { units and } V_{y}=-7.40 \text { units, determine the magnitude and direction of } \overrightarrow{\mathbf{V}} \text {. }$ magnitude    units direction    $^{\circ}$

Graphically determine the res *gqh4xfoo,2dpaghf u0 ta/k8 (( pdn5ultant of the following three vector displacements: ( ,q 0f4gk8onh*pad2 /xfphgtdau( (o51) $ 34 \mathrm{~m}, 25^{\circ} $ north of east; (2) $48 \mathrm{~m}, 33^{\circ}$ east of north; and (3) $22 \mathrm{~m}, 56^{\circ} $ west of south.

  The components of a vecty2 gb:dxyj6zuld99h 8or $\overrightarrow{\mathbf{V}}$ can be written $ \left(V_{x}, V_{y}, V_{z}\right)$ . What are the components and length of a vector which is the sum of the two vectors, $ \overrightarrow{\mathbf{V}}_{1} $ and $\overrightarrow{\mathbf{V}}_{2}$ , whose components are (8.0,-3.7,0.0) and (3.9,-8.1,-4.4) ? components (a,b,c) a =    b =    c =   
length   

  $\overrightarrow{\mathbf{V}}$ is a vector 14.3 units in magnitude and points at an angle of $34.8^{\circ} $ above the negative x axis.
(a) Sketch this vector.
(b) Find $V_{x}$ and $V_{y}$ .$V_{x}$ =    $V_{y}$ =   
(c) Use $ V_{x}$ and $ V_{y}$ to obtain (again) the magnitude and direction of $\overrightarrow{\mathbf{V}}$ . magnitude =    direction =    $^{\circ}$ above - the x axis
[Note: Part (c) is a good way to check if you've resolved your vector correctly.]

  Vector $\overrightarrow{\mathbf{V}}_{1}$ is 6.6 units long and points along the negative x axis. Vector $\overrightarrow{\mathbf{V}}_{2} $ is 8.5 units long and points at $+45^{\circ}$ to the positive x axis. (a) What are the x and y components of each vector? (b) Determine the sum $\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{V}}_{2}$ (magnitude and angle)

$ (a) V_{1 x}$=   units $V_{1 y}$=    units $V_{2 x}$=    units $\quad V_{2 y}$=    units


$\left|\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{V}}_{2}\right|$=   units $ \quad \theta$=  $^{\circ}$

  An airplane is traveling c. ftt)u s9j5 qqaof)7$735 \mathrm{~km} / \mathrm{h}$ in a direction $ 41.5^{\circ} $ west of north (Fig. 3-31). (a) Find the components of the velocity vector in the northerly and westerly directions. (b) How far north and how far west has the plane traveled after 3.00 h ?(a ) $ v_{\text {north }} $=   $v_{\text {west }} $=    (b) $\Delta d_{\text {north}} $=    $\Delta d_{\text {west}}$ =   

  Three vectors are shown in Fig. below. Their magnitudes are given in arbitrary u)i7ca44w -nks nnrq5bnits. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with t rnn)i an5cwk7q-b4 4she x axis.


$(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}})_{x}$ =   
$(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}})_{y}$ =   
$|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$

  $\text { Determine the vector } \overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{C}} \text {, given the vectors } \overrightarrow{\mathbf{A}} \text { and } \overrightarrow{\mathbf{C}} \text { in Fig. below}$



$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$

  (a) Given the vectorf,7dbxvyr(a j 2)b b:bs $ \overrightarrow{\mathbf{A}}$ and $ \overrightarrow{\mathbf{B}}$ shown in Fig. below , determine $\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}$ . (b) Determine $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}$ without using your answer in (a) . Then compare your results and see if they are opposite.


$|\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}|$ =   
$\theta_{B-A}$ =    $^{\circ}$above -x axis
$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|$ =   
$\theta$ =    $^{\circ }\text { below }+x \text { axis }$

  $\text { For the vectors given in Fig. 3-32, determine (a) } \overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}} \text {, (b) } \overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{C}} \text {, and (c) } \overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}} \text {. }$




$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$ below +x axis
$|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$
$|\overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|$ =   
$\theta$ =    $^{\circ}$ below - x axis

  $\text { For the vectors shown in Fig. below, determine (a) } \overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{A}} \text {, (b) } 2 \overrightarrow{\mathbf{A}}-3 \overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{C}} \text {. }$



$|\overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{A}}|$ =   
$\theta$ =    $^{\circ}$ below - x axis
$|2 \overrightarrow{\mathbf{A}}-3 \overrightarrow{\mathbf{B}}+2 \overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$ below + x axis

  The summit of a mountain, 2450 m above base camp, is measured o fu5bxm3p jjnt*ua ljxj7:,h. c61n -ln a map to be 4580 m horizo:u uph7n,jj j3 1xn ft.mbxl5a*-6cl jntally from the camp in a direction $32.5^{\circ}$ west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north, and z axis up. x =    y =    $|\overrightarrow{\mathbf{r}}|$ =   

  You are given a vector in the xy*ioj7v- 7nkat plane that has a magnitude of 70.0 units and a y compon n7ak i7*o-jtvent of What are the two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a speed of How far fron(3o7bqa2r6/ khhoj d m the base o(63 n/r2oadjqkboh7 hf the rock will she land?    m

  A diver running dives out horizontally from the edgpkvqk38b 0 se i)f9x)63,; c9wr;zff lmjzhhte of a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its b09zfcb;qfzjt xf,9p)r 8 vw)ke hlhk36 i;sm3ase did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water at a speed of At what angle(s)-l a0,x,ifl2i b+nnmx should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch , l2i0mbn+a n lx-fx,ithe two trajectories.

  Romeo is chucking pebbles gently up to Juliet’sr0g3p h /n c :0ys+ltnpoqco3lhl17*i window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the es1cn0li7op/ yo0 nlpg3 q3 h tl:+*rhcdge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontabi4.gir /r h3m,nz o4dlly from the roof of a building 45.0 m tall and lands 24.0 m from the base. What was the ,mgh/dn.4io rr4 z3 ibball’s initial speed?   

  A football is kicked at ground level with a speed of 18.0ya h f2ti( we/x-5g1,gwt8nyl $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontall.n v;u )t fsr+fmy2 + kw5kwei(x/gwj8y at from the roof of a building lands 36.0 m from the ygw);/km8e rxi5(jt un 2k.v +sff+ wwbase of the building. How tall is the building?    m

  An athlete executing a long jumm lau ;ooto6e6rx)3i(5hz kxw 9o(rs6p leaves the ground at a 28.0$^{\circ}$ angle and travels 7.80 m .
(a) What was the takeoff speed?   
(b) If this speed were increased by just 5.0 % , how much longer would the jump be?   

  Determine how much farther a person can jump on the Moonpkgse o4+)q6 m as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravi )pes6+k qgo4mty on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at 9j il9bs.;c3 rwl (ftxa target (on the same level) 75.0 m away.
(a) If the bullet leaves the gun at a speed of by how much will it miss the target?  
(b) At what angle should the gun be aimed so as to hit the target?    $^{\circ}$

  The pilot of an airplane traveli2; cmpdq.,p b-;1fsu pr.yois ng wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds bef.;.ds, mrsqpcfp p i- 1b;ouy2ore the plane is directly overhead?    s

Show that the speed with which a projectile leaves the ground is equal to its speed just before it strikes the ground at the end of its journey, assuming the firing level equals the landing level.

  A projectile is fired with an initial speed ofu0agv.5z6 ydax lqs+i 2karf:y,o) k4 at an angle of 34.5$^{\circ}$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot from the edge of a cliff 125 m above ground level with anw edrt n4 l(5lu*+,qbv initialurw4d b*qe( nv 5t+,ll speed of at an angle of 37.0º with the horizontal, as shown in Fig. below.
(a) Determine the time taken by the projectile to hit point P at ground level.   
(b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find   
(c) the horizontal and the vertical components of its velocity,   
(d) the magnitude of the velocity, and   
(e) the angle made by the velocity vector with the horizontal.    $^{\circ}$ below the horizon
(f) Find the maximum height above the cliff top reached by the projectile.   

  A shotputter throws the sj,d6 3k(g ,sexg -bp+jkk(ppu hot with an initial speed of 15.5 $\mathrm{~m} / \mathrm{s} $ at a $ 34.0^{\circ}$ angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 m above the ground.   

  At what projection angle will the range of a pdj )bh-58fkssq 6zf/i rojectile equal its maximum height?/qkz-i 68s sffh5)jbd    ${\circ}$

Revisit Conceptual Example 3-7, and assume that thovtny9s k*d(- e boy with the slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by lettingvk9 (-y not*ds go at the moment the water balloon is shot.

  A rescue plane wants to drop supplies to isolated mountain climberxuryb ;+esk.l.i,+m es on a rocky ridge 235 m below. If the plane is traveling horizontall e+. m;kb+.ry isxu,ley with a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

(a) how far in advance of the recipients (horizontal distance) must the goods be dropped (Fig. a)?    m
(b) Suppose, instead, that the plane releases the supplies a horizontal distance of 425 m in advance of the mountain climbers. What vertical velocity (up or down)  ----待选择----updown  should the supplies be given so that they arrive precisely at the climbers' position (Fig. b)?    m/s (fill in magnitude here)
(c) With what speed do the supplies land in the latter case?    m/s

  A person going for a mor5fkdw 8 np46 6see6mupd(vbg(ning jog on the deck of a cruise ship is running toward the bow (front)k pvf 8m6(pn 6bus64dg(5eew d of the ship at 2.2 $\mathrm{~m} / \mathrm{s}$ while the ship is moving ahead at 7.5 $\mathrm{~m} / \mathrm{s}$ . What is the velocity of the jogger relative to the water?    m/s
Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?    m/s

  Huck Finn walks at a speed of 0.6sldlhn*2;b/juw z0 )setp 66u0$ \mathrm{~m} / \mathrm{s}$ across his raft (that is, he walks perpendicular to the raft's motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.70$ \mathrm{~m} / \mathrm{s}$ relative to the river bank (Fig. 3-38). What is Huck's velocity (speed and direction) relative to the river bank?Magnitude =    Direction =    $^{\circ}$

  You are driving south on a highway at e .xbu8w)f*0fbm*+mr f*x u q,mqmt:e 25 $\mathrm{~m} / \mathrm{s} $ (approximately 55$ \mathrm{mi} / \mathrm{h} ) $in a snowstorm. When you last stopped, you noticed that the snow was coming down vertically, but it is passing the windows of the moving car at an angle of $30^{\circ} $ to the horizontal. Estimate the speed of the snowflakes relative to the car    and relative to the ground.   

  A boat can travel 2.30ku)h4* 8fecm6jg4 lnd$ \mathrm{~m} / \mathrm{s}$ in still water.
(a) If the boat points its prow directly across a stream whose current is 1.20$ \mathrm{~m} / \mathrm{s}$ , what is the velocity (magnitude and direction) of the boat relative to the shore? magnitude    direction    $^{\circ}$
(b) What will be the position of the boat, relative to its point of origin, after 3.00 s? (See Fig. below)diraction =    awayfrom the starting point,angle =    $^{\circ}$ relative to the shore

  Two planes approach each other head-on. Each has a speed o;v6ho-d9 cinujyr(: o pf0xt-5ulz x0f and they spot each other when they are initially 11.0 km apart. How much tix n zf00ltj( h;yu-6 id: 9c-5uopxrovme do the pilots have to take evasive action?    s

  An airplane is heading due south at a speed of ojux )-91bjja600$ \mathrm{~km} / \mathrm{h} $. If a wind begins blowing from the southwest at a speed of 100 $\mathrm{~km} / \mathrm{h}$ (average), calculate:
(a) the velocity (magnitude and direction) of the plane relative to the ground, and    $^{\circ} $ east of south
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.   
[Hint: First draw a diagram.]

  In what direction should the pilot aim the plane in Problem 41 so dvn o5 qjb:7c5k)wb0ithat it will fly due southv:0 5icj5kbdnoqw 7)b?    $^{\circ} $ east of south

  Determine the speed of thj6q,-;go 5 vq,zrdr7upip y/he boat with respect to the shore in Example 3–11.   

  A passenger on a boanv 6qwo,,xj )tt moving at 1.50$ \mathrm{~m} / \mathrm{s}$ on a still lake walks up a flight of stairs at a speed of 0.50 $\mathrm{~m} / \mathrm{s}$ (Fig. below). The stairs are angled at $45^{\circ}$ pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?   

  A motorboat whose speed in still*,.r* xp 9d) qksinbxz water is 2.60 $\mathrm{~m} / \mathrm{s}$ must aim upstream at an angle of 28.5$^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current?   
(b) What is the resultant speed of the boat with respect to the shore?   

  A boat, whose speed in still0 :q/amp n*4m/73uzklhmtfog water is 1.70 $\mathrm{~m} / \mathrm{s} $, must cross a $260-\mathrm{m}$ -wide river and arrive at a point 110 m upstream from where it starts (Fig. below). To do so, the pilot must head the boat at a 45$^{\circ}$ upstream angle.


What is the speed of the river's current?   

  A swimmer is capable of swimminc )zzn 0zfoq8y-in4,pg 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?   
(b) How long will it take her to reach the other side?   

  A swimmer is capable of swijehmjy1hy:q-d2d h.7 r 86x;sr ug ,dpmming 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?    $^{\circ} $
(b) How long will it take her to reach the other side?   

  An airplane whose air speed i:zf n 67(w7qs10szmktf q)m hrs 620$ \mathrm{~km} / \mathrm{h}$ is supposed to fly in a straight path 35.0$^{\circ}$ north of east. But a steady 95$ \mathrm{~km} / \mathrm{h} $ wind is blowing from the north. In what direction should the plane head?    $^{\circ} $ north of east

  An unmarked police car, traveling a constanv9lh0m tf4i jn u/r(;at 95$ \mathrm{~km} / \mathrm{h}$ , is passed by a speeder traveling 145$ \mathrm{~km} / \mathrm{h}$ .

Precisely 1.00 s after the speeder passes, the policeman steps on the accelerator. If the police car's acceleration is 2.00 $\mathrm{~m} / \mathrm{s}^{2}$, how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)?   

  Assume in Problem 50 that sw2s*v xh4(a1h;j3 jg s +lxn*m /onnrthe speeder’s speed is not known. If the police car accelerates uniformly as given above, and overtakes the speeder after +1;3 n/(anhj2vlx xmj* sr*4hgsow ns7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner at.d-) so+bke*8et ctww right angles to each other (Fig. below). Car 1 travelse*w-) +8okdetc bwt .s at a speed relative to Earth $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , and car 2 at $v_{2 \mathrm{E}}=55 \mathrm{~km} / \mathrm{h}$ . What is the relative velocity of car 1 as seen by car 2 ?    km/h    $\theta$$^{\circ} $ West of North
What is the velocity of car 2 relative to car 1 ?    km/h    $\theta$ $^{\circ} $ south of east

  William Tell must split (caggwg f1xs(ie:b 5y/+ hjg9the apple atop his son's head from a distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At: i+ghc1 gwyx gg(sbe( /5f9aj what angle must he aim it to hit the apple if the arrow travels at a speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 2t.23p+f/w85zpad x i2p pv .bxvp+xhk5 m south, and then takes an elevator 10 m down in/d .v2+tih3 pp8zfa2bp x.v+p kwx5xpto the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

The result is that the displacement is    m , at an angle of    $^{\circ}$ South of East, and    $^{\circ}$ Below the Horizontal.

  On mountainous downhill roads, escape routes are sometimes pla 5wlydw hl1s4c*1 1okdced to the side of the road for trucks whose brakes might fail. Assuming a constanth11l5 wslod k4*cdw1 y upward slope of 32$^{\circ}$ , calculate the horizontal and vertical components of the acceleration of a truck that slowed from 120 $\mathrm{~km} / \mathrm{h}$ to rest in 6.0 s . See Fig. below

$\text { The horizontal acceleration is } a_{\text {hoiz }}$ =    $\mathrm{m} / \mathrm{s}^{2}$
$\text { The vertical acceleration is } a_{\text {vert }}$ =    $\mathrm{m} / \mathrm{s}^{2}$

  What is the y component of a vector (in the x y plane) wh kzlcjn43j :dt+ asldca +2:v3ose magnitude is 88.5 and whose x compoa2aljc:+ldjkz st 3n:v +c d34nent is
75.4? What is the direction of this vector (angle it makes with the x axis)?
$\text { Direction }$=    $^{\circ}$$ \text { relative to } x \text { axis }$

  Raindrops make an angle yc0wue4sb1tyf4;gm, rg9 ,vy $\theta=30^{\circ}$ with the vertical when viewed through a moving train window (Fig. below). If the speed of the train is $20 \; m/s$ (a) what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically?    $m/s$
(b) what is the speed of the raindrops relative to the train?    $m/s$

  A light plane is headed 7f8hy1 llj. vvdue south with a speed of 155$ \mathrm{~km} / \mathrm{h}$ relative to still air. After 1.00 hour, the pilot notices that they have covered only 125 km and their direction is not south but southeast $\left(45.0^{\circ}\right) $. What is the wind velocity? $v_{wind}$ =    km/h $\text { The direction of the wind is } \theta$=    $^{\circ} $ north of east

A car moving at 95 viv4g .r/ gnybr.4i4s$\mathrm{~km} / \mathrm{h}$ passes a 1.00$-\mathrm{km} $-long train traveling in the same direction on a track that is parallel to the road. If the speed of the train is 75$ \mathrm{~km} / \mathrm{h} $, how long does it take the car to pass the train, and how far will the car have traveled in this time? What are the results if the car and train are instead traveling in opposite directions?

  An Olympic long jumper is capable of jumping 8.0 m . Assume8kdd dv *)y7bing his horizontal speed kdbde yv7d8*)is 9.1 $\mathrm{~m} / \mathrm{s} $ as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright - that is, the same way he left the ground. t =    y =   

  Apollo astronauts took a ak + x,a 7lzlzjh:c 1po;zc4z3“nine iron” to the Moon and hit a golf ball about 180 m! Assuming that +chxpjl z7zao3 ,a;1 :lzz4ckthe swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over the 7.wl20 vb;4 vww*xhnvm( 5$-\mathrm{m}$ -high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat?    Assume the ball was hit 1.0 m above the ground and its path initially made a 38$^{\circ}$ angle with the ground.

  The cliff divers of Acapulco push off horizontally from rock platforms aboyo u:g5zk;3b*4bi tzput 35 m above the wg u* bz;poy5tkzib43:ater, but they must clear rocky outcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. below. What minimum pushoff speed is necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontally. What minimum speedjoeu-xz0 cb. . is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is “launched.xj ez0c.ou- b” from a height of 2.50 m? $\approx$    Where will the ball land if it just clears the net (and will it be “good” in the sense that it lands within 7.0 m of the net)? How long will it be in the air? $\approx$    See Fig. below.

  Spymaster Paul, flying a s,pu )j2 b6a8cssap43-d obzbconstant $215 \mathrm{~km} / \mathrm{h}$ horizontally in a low-flying helicopter, wants to drop secret documents into his contact's open car which is traveling 155$ \mathrm{~km} / \mathrm{h}$ on a level highway 78.0 m below. At what angle (to the horizontal) should the car be in his sights when the packet is released (Fig. below) ?



$\theta=\approx $   $^{\circ}$

The speed of a boat in still water is v . The boat is to makmy 7yqbx u.6,56u.0 3wnafpdapw,k xae a round trip in a river whosnmaax u0,bw73 ua py.d.p x,yq56kwf 6e current travels at speed u . Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving (a) upstream and back downstream, (b) directly across the river and back. We must assume u

  A projectile is launched 9mb y y5wnoo;zek l,/+*ce)+j6wvsjlfrom ground level to the top of a cliff which is 195 m away anmkjbl;j, oy ) v+6l*czyo w+s5w9een/d 155 m high (see
Fig. 3-47). If the projectile lands on top of the cliff 7.6 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance.



$v_{0}$=    $ \mathrm{~m} / \mathrm{s}$
$\theta$=    $^{\circ}$

  

(a) A skier is accelerating down a 30.0$^{\circ}$ hill at 1.80$ \mathrm{~m} / \mathrm{s}^{2} $ (Fig. 3-48). What is the vertical component of her acceleration?    $m/s^2$
(b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 335 m ?    $s$

  A basketball leaves a player's hands at a height of 2.10 m above the floor.9p5fp c6s tc+;3bqx2i r6q pnf The basket is 2.60 m above the floor. The player likes to sh5c6cqps;qf6xt3 p2frinb + 9poot the ball at a 38.0$^{\circ}$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22 \mathrm{~m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves the xi*qlp-te9yjz )n 3*l end of a $5.0-\mathrm{m}$ -high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine
( a ) her initial velocity, $ \overrightarrow{\mathbf{v}}_{0}$ ,    ${ }^{\circ} \text { above the horizontal }$
(b) the maximum height reached,   
(c) the velocity $ \overrightarrow{\mathbf{v}}_{\mathrm{f}}$ with which she enters the water.    $^{\circ} $ $\text { (below the horizontal) }$

  A stunt driver wants to make his car jump over eight cars parmi*gjbmc9an(q e549u20 d* q-m sdmlaked side by side below a hormmmdn90q*5 aices9a -mdu jgl(2b *q4izontal ramp

(a) With what minimum speed must he drive off the horizontal ramp? The vertical height of the ramp is 1.5 m above the cars, and the horizontal distance he must clear is 20 m .    $m/s$
(b) If the ramp is now tilted upward, so that "takeoff angle" is $10^{\circ}$ above the horizontal, what is the new minimum speed?    $m/s$

  A batter hits a fly ball which leaves the bat 0.90 m above the grop-9fcgumfy9w .4vl(p rrw:v 2und at an angle fprmglycp f 29 w9-(w:.vru4vof $61^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s} $ heading toward centerfield. Ignore air resistance.
(a) How far from home plate would the ball land if not caught?   
(b) The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level.

Find his speed.   

  At t=0 a batter hits a baseball with an initial speed o fv jy(z6c*ma17q.+ ibhtzhy7h:vmf1 f $32 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    $^{\circ}$

  A ball is shot from the top of a building ;u ; mvdf4pw(-hml-hgwith an initial velocity of 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart gun, and being a clever physics studenqsbr5 55mju )i-abcvb z.b,sy9,fi0a t you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and itm-bsj9v iiz ,.,a br 0a)bsb 5y5fcuq5 takes 4.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?