One car travels due east at and a second car travels north at Are theirf kstyljm b6cz c1aw+-t (;)f/ velocities) tk(f fl/cbjc tm ay+1-6;wsz equal? Explain.

Can you give several examples of an object’s motion in whi2v w9a7, 6k:chod ldioch a great distance is traveled bu6k2wl,dv:79hda co oit the displacement is zero?

Can the displacement vector fo a + jzbsv/2mojcaa ku;b/509or a particle moving in two dimensions ever be longer than t+vab koj u25sm/0ao ;9ba/cjzhe length of path traveled by the particle over the same time interval? 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 length xnc ,:h8aduub5 up+.k$ 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 give t;6idt imlbrt ,5g4 j.hhe zero vector? Can three unequal jtd l .,;brti6imhg45 vectors? Under what conditions?

Can the magnitude of a vector ever (a) be e 8o*t h,d+wcjl,bsa: nqual to one of its components, or (b) bn8o:*aw l,sh+c,dtbj e less 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 first hop onto u 0z(g ;uyul+mf;h+-r5hx 3 ib0mkcp ua moving walkway and then onto the cars themselves. Whyuumu i+ 3 hg 0-(h5rbpcu+0;fylkxm ;z is this done?

If you are riding on a train h5 9lrimd18twwo9 cg9gek*,sgh 5 g j1that speeds past another train moving in the same direction on an adjacent track, it appears that the other train is moving backward. Why?* ogc w9l8mi51g dhg5kg9 1,wejhrst 9

If you stand motionless under an umbrella in a rainstorm where the drops fall:rysa,b. r(/vuljs (z vertically, you remain relatively dry. However, if you start running, the rain begins to hit your legs even if they remain under the umbrellz sj / y:(rvla,usb(.ra. Why?

  A person sitting in ans qp+b l+i,2+4l o6dvzaz5yt /iiih 9a enclosed train car, moving at constant velocity, throws a , v z/psl5 24o+ iq6hb+9zt+iialyaidball straight up into the air in her reference 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, ke sxyfv1b)mt:7d,y- set off across a river at the same time. A heads straight across 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 xmseyyd 17-b,):tfv k point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a ba)5 gmg i0qs)ozsukw 0.seball player “judges” the flight of a fly ball? Which equation i .oz) 0gikq5sw0sg )umn this Chapter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the target? How shouldae0ur5 anb f dh2 4kuxk*ie)26 your angle of aim depend on the distai6)e2540e nrbfa u2xk* hkdu ance to the target?

  A projectile is launched at an angle of c7k (p6af;vza $30^{\circ}$ 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 inite-) czka7csgk6vq9 nut+ (wb. ial speeds, bcezk9+v .w( - skctb7g6)uqnaut with $ \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 *qkm.4 i(nh6 *b6lx k+juyn usb9ja3wkm southwest. What is the displacement of the car from the point of origin (magnitude and direction)? Drakm*js ix64buh kqn.y3( 6n *a9bl w+ujw a diagram.

  A delivery truck travels 18 blocks north, 10 blocksfaz;5a uzvg s : cwso2(hkx.2hbu 8n3* east, and 16 blocks south. What is its final displacement from the origin? As *nw3k x shusfa2g u a:;.2ovb5cz(8zhsume the 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 resultantqh s(ag ab ( g:k.a;suyel zey74:y-m4 of the following three vector displacements: z ;ag -7yqhl4ks((yusay 4ea.e::g bm (1) $ 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 vec.v1oj.zmf4 qjtor $\overrightarrow{\mathbf{V}}$ 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 trave1toq99jsroo8pc / p*e ling $735 \mathrm{~km} / \mathrm{h}$ 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 ini8dy0fenp a.f +s03uo Fig. below. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) componnidsfap00y f 3+8u.oe ents, (b) magnitude and angle with the 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 vectorsz+ w4 9;0-k* jzkqruj*liakk a $ \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 on ar sw8i. )55-ni sbjeis map to be 4580 m horizontally from the camp in a di8 ni .s5-i) rs5iebswjrection $32.5^{\circ}$ 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 plane that has a magnitude2kl :8odd1 vn gp6g;nv of 70.0 units and a y compon 8kvlg1:n2 gdndvop6;ent of What are the two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-a bubf 4(3idjs5y*-nuhigh rock with a speed of How far from the base of the rock will she ladu-yb5ji na f3ubs(4* nd?    m

  A diver running dives out horizondcvw ar yhd:)k c7063otally from the edge of a vertical cliff and 3.0 s later reaches the water below.:6ycrdo )d7whc a3k 0v How high was the cliff, and how far from its base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water a;t c)0 z1bfv3 lp01bmgwwo4a(cdn24in, lzp r t a speed of At what angle(s) should the nozzle point in order that the water land n1pr n;pvzfltwbc (gdio0l,wa2 m1 4c)34b 0z2.0 m away (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles geqea grztc lz1f)0dt9 ;bod f/ )jutea-,354qk ntly up to Juliet’s window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge 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 )qzlf;-,f 0 rektqt1/db t gaj9 4adzu) 5eoc3they hit her window?    m/s

  A ball is thrown horizontally from th,cse;6d *cy3t gxnb;y5 7jr nie roof of a building 45.0 m tall and lands 24.0 m from the base. What was the b;ygbj3t6sd 5 *erni7c n xy;c,all’s initial speed?   

  A football is kicked at ground level with aut8lmj15ws1 hyb91i:2lp kx1- mfr u t speed of 18.0 $\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 horizontally at from the pmh1f 0wl(6eo zi)r2wh*m.zi*cka 5f roof of a building lands 36.0 m from the p5izw(f) *l.1*cako imwz0mfrheh62 base of the building. How tall is the building?    m

  An athlete executing a long jump leaves the ground at a;zxsth7:b q1 )aua)sc 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 canp i 6+miczjg w 0r3bn+aj .zcrpo8;8o( jump on the Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the .+ 3jipi 88( oobc6zrz+rg0 mwjcnp;a Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 75.0 ma .wd c jlez;.0qa:6od 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 traveling wantff7de :pjt62 xs to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be ted7f:2p jx6 fdropped how many seconds before 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 of at an ang47tie :d3 y tgk bz3 4l-a2e3z3ffsxjjle 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 12vkc xysf w6w/-l-0 fq,5 m above ground level with an initial speed of at an angle of 37.0º with the horizontal, as shown w0-cqyfsfvl-6 kx/,w 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 shot with an initial speed of 15.5 v i :h 3g/+wajsc-jxp-c t,sf /xaf-s;$\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 an.jow1vl4z/ hopf,mh- 9.j us ngle will the range of a projectile equal its maximum height?. zhov- husmnjw9pfj/l1.o 4 ,    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the slingshotn9ni do*, zin-+kg q5k 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 letting go at the moment the water balloon is ski nn qo+zk5,g- 9ndi*hot.

  A rescue plane wants to drop suppliqtc-:1)vb tbf 7ngw 4res to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with a speed ot1:)fvbcq4wb -r 7ngtf 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 morning jgs* kx/ wl,tm4og on the deck of a cruise ship is running toward the bow (front) of the ship at 2.x4*,t wkls/mg 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 ogbo ;i+ft-q(h5(x lon f 0.60$ \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 onkum5q2v ,o+hdit /0mj/d(xtn a highway at 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 2.3* ) x.;,wwdlkv cr req5s*up-x0$ \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 of as1 hmoa;km64 g-jzosav/4lk ,56ebe n nd they spot each other when they ooh56g-em/ njab1k em6sal,4v;kz4s are initially 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is heading duel e wgq7jbikd.x;s:,1 south at a speed of 600$ \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 9f o;ua5 n0bcy+ y8 qw.g5jwbyProblem 41 so that it will fl5y.ugb f 8+ywcn ;05jbayo w9qy due south?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shore b 6 1x;1bmacttin Example 3–11.   

  A passenger on a boat moving 9z; cr;tmivc4 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 water re4 ;u.xe85;zkojqu lis 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 still water is 1..r7*ohg vy;l 06e4g mlws(qcx70 $\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 swimm2l6h rl +)rsh- jpoyxj. ep+u*ing 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 swimming 0g,gd,;zb o f+y.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 speedhe-6l*ex6o3 rw ubjg( is 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, travelinge b.zetoiqm9m-ktc7-(oj5aig3- u6 p a constant 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 thti bh49 87b/2 psgdtvde speeder’s speed is not known. If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was thev87tdgp d9sb 4hibt2/ speeder’s speed?    km/h

  Two cars approach a street corner at right angles to eachm. wnif(,q nsl)w7q2v other (Fig. below). Car 1 travels at a speed relative to Earth .swmn2q,nv( l) iqw7f $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , 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 th .lo+y6 a 2zxsqvkd)d;e apple atop his son's head from a distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speeqsldz)y;6d v2+a k. xod of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25 m south,id2k q./fvq+bsn)n 3f and then takes an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber rela nv q)kn.q/fi2b+ df3stive 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:ln /rss63*vjwi ri+z placed to the side of the road for trucks whose brakes might rli :6+ v*ws/nijs3z rfail. Assuming a constant 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)8s 5i4qj6wcwrk+u z 7r whose magnitude is 88.5 and whose x compswruj iwc+ 8q5kzr7 46onent 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 anglmt79c 0x:niuhyydx)i7b, r/ ie $\theta=30^{\circ}$ 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 due south with a speedum igrw/;h +x+ 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 tzr jhwh3,ls f1+:6om 3juek0$\mathrm{~km} / \mathrm{h}$ 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 tz )hhkz 33ek-jumping 8.0 m . Assuming his horizontal speed is 9kzh)zk h-3et3 .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 “nine iron” to the Moon and hit a golf ballakg pw8 z,;lmk7;pai + about 180 m! Assuming that the swing, launch angle, and so on, were the same as on ;k8agwi+ mlkpz,;pa7 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 6f7fho e /jp6bl5 o-ll9 d55b7c psbdrover the 7.5$-\mathrm{m}$ -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 Acap aq*cqi pweh.*35wfm taswytmf,20.1 ulco push off horizontally from rock platforms about 35 m above the water, 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 point0mm2*pwqt fs.1i*wf c ty5ewqa 3,.ha. 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 hort0zh4xve5o f y:0/ c pi0f/lerizontally. What minimum speed 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” fromi0/ exp4l:ft5v0y 0fc/e rhz o 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 constantyw60gv; fvf/ h $215 \mathrm{~km} / \mathrm{h}$ 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 make a uomk 4g 6dw3+tround trip in a river whose6k+ d3om ug4wt 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 from ground level uv x um.hh+ar09 2gx7jb/g0psto the top of a cliff which is 195 m away and92s+j0.xgu0hv/7hbxu p g amr 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 3)ffbri *gq;ga height of 2.10 m above the floor. The bbqg;ffri*) 3 gasket is 2.60 m above the floor. The player likes to shoot 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 end 2r fflt )ko u;4tyd:1jof 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 ovew-fexg;5 v fub;h c6w75szh v+r eight cars parked side by side below a hx z wh6bh;+- ;fvsvw7cu5g 5feorizontal 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 gro-gco ag)r usxrk sk 1k:uoxq+xv)8e- - hh498vund at an angle a eghru ) suxr-9s +o)kv8 :qvxg--k c81kox4hof $61^{\circ}$ 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 spep6n cu;w* 5kbjed of $32 \mathrm{~m} / \mathrm{s}$ 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 with g ))f e-ug :w, *c/eaygn 912kyiwscduan 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 4li gi ffvb)cc1.1,u qzgu9s2e-; bz vgun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You izf1z,u).1e-bsi 4gcuclv qbg; f9 2vshoot the gun straight up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?