One car travels due east at and a second car travels,e6gy2 yxjl-y north at Are their velocities equal? Explainyj26l-, yxg ye.

Can you give several examples of an object’s motion in whia8 dk f26opn;uch a great distance iskdn;8a p6ufo2 traveled but the displacement is zero?

Can the displacement vector for a particj iy,g: j68style moving in two dimensions ever be longer than the length of path,ji 6 gyt8sj:y 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 t) 2qri5/ wzvu$ 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 the zero vectorlopjz sliaj bq0( ep2+7t-vc9 pe0y13dm90x g? Can three unequal vectors? Undersj q(1mp02lie 0td0 vy lap9ec 3jzo-g+xp79b what conditions?

Can the magnitude of a vector ever (a) be equal to one of its -xu h9lz856xpqd dd8 m9kr :lccomponents, or (b) be less than one of its componl 5hd8mkzc9d9r l-u 6xqxp:8dents?

  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 ont3aa c *m.w/yw o;nw,.lursa )to a moving walkway a),a aw.no3s .uy/tc*;m wrwalnd then onto the cars themselves. Why is this done?

If you are riding on a train that spvr8x9-m 7u fa*s8 mf3/bt dcrveeds past another train moving in the same direction on 8 f*3rvrfs9vau8t m 7x-c dm/ban adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under an umbrella in a rainstormb6 fw if-:8rbfe leg*; where the drops fall vertically, you remain relatively dry. However, if you start running, the rain begins to hit your legs even if thfr8* ;f6gb fi:b- weleey remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at constant velocity, throwtf9y6u s1mar +s a ball straight up into tht9+1 6yum asrfe 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 acxq -ny .cse- c dop8,x (ul(t0/rwd2same speed in still water, 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 poin2d8x p,a cetyw.cx(r--o udn/c0q (lst. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baseball player “judges” the flight of a fly bk6nq(tvmu02i oxuqxw1q + ruv4u 3 o..all? Which equation in this Chapter becomes part of the player’s 6qq u1w(xo 2n mqruv.x+0.u o utk4i3vintuition?

In archery, should the arrow be aimed directly at th)+boac9fn:yt 6g )j bce target? How should your angle of aim depend on the :jgocbt6)nc )9 + fbaydistance to the target?

  A projectile is launched er +6 gze5r-kbat an angle 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 sp.z9h ilq s xc)x0)pe8geeds, but08gi)x l.ce)qhp zxs9 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 x s.uss 15.as+tvz4n hg3 b(*qnv7cn hthen 85 km southwest. What is the displacement of the car fusghb5x(+csnsvz 7 *4n.n 1.h3tavqsrom the point of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10ocu * gq20rw)c(gi3z x blocks east, and 16 blocks south. What is its final displacement from the origin? Assume the blocks arcw(3xqzio) 2crgg*u 0e 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 resultant of the fy),k:;tbvqc oollowing three vector displacements: (1: ;tvc),y oqbk) $ 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 vectehl99 pw8bq 6dy 5g io,4trf4nor $\overrightarrow{\mathbf{V}}$ 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 stmk)u9r ;n( pg /-dlr:ggc;ohgc(i 6 $735 \mathrm{~km} / \mathrm{h}$ 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 arehkqim ), .60trnra v1j given in arbitrary units. Determin) ,a.j60vmr1nhki qrt e the sum of the three vectors. Give the resultant in terms of (a) components, (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 vectors 3wb3 7 *zl4a:7hqbla fjm8rqi$ \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 alk) 1ay +- tax6 onnvvml7/ht+bove base camp, is measured on a map to be 4580 m horizontally from the camp in -k) o +nxal6+myl1v/ntt7 avha 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 plane tha 0wyh5qgiv4r,t has a magnitude of 70.0 units and a y component of What 4yw r,v5qi g0hare the two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-b ,kwlt+21x o3r. j7dl)dtjbw high rock with a speed of How far from the base of the roc ,jjldrt) .xkd71 b23 +btowwlk will she land?    m

  A diver running dives out horizontally from the edge of a vertm 2+fne.te, q6be fi.kical cliff and 3.0 s later reaches the water below. How high was the cliff, and hne+2i k6fbq m.e,tef .ow 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 at a speed of At what angle(s)n+pq ; cwn: *v*jvw(hh should the nozzle point in order that the water land 2.0 m away ;v:w* jw(qh+ npn*vch (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently u,nj+q f7zsjj vd* t(z-p 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 anddz z-j,s+qjj nv7(*f t 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 horizontally from the roof of a building 45.0 m tall and lands rk.vy +g7*,)mr* 8g,e i dl(grsww cap24*ggpgy+.v m,ri rw r(l*8e,wsacdk7) .0 m from the base. What was the ball’s initial speed?   

  A football is kicked at ground level winrh /ulbq0f2 i1a*uc u +78icath a 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 roof of a building lands 36.x46 /vdsbkcb;kfkgk(l 8yitpc4 c 3a+05z x ,i0 m from the fz(g;cdik 3ctks4bivcpx0 a+ 8kkbx4,5/y 6 l base of the building. How tall is the building?    m

  An athlete executing a long jump leaves the ground at a ; ay:cbqkern)51i -f fr3a+uc28.0$^{\circ}$ 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 Moon as compared to tnxoh5y fts;1 m0dy l9(j8ja0 khe Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moon is one-sixth what it is oy (08j of1lknd x5as0j;h9mtyn Earth.    times

  A hunter aims directly at a target (on the same l1z-w0d9)s nm bch;yzcayz2 y)evel) 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 traveling wants a8sc4,g .qju cto drop supplies to flood victims isolated on a patch .qgau sccj4,8 of land 160 m below. The supplies should be dropped 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 angle ;ya upx )ht4sku*fxtd 38ca:*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 an ie5 5 5:fypa )mr uziq sw9r*)t/0v rpllw1kdz,nitial speed of at an angle of 37.0º with the horizontal, as shown in Fig. belowa p5lur1)05)yedvtlw, /p:sk9riw5 z*qrm zf .
(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 j qw.ygnyl,+- 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 projectile eqas3 23cws(pr6.a hire ual its maximum height?a3r2.p(cse ir3 6haws    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the swxp /+ b;5y +lwe)yqrhlingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tr+;wybph5ex rw l/+) yqee. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants to dr; 3lt/vws tfniz ) j2ftbx.7g,op supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally wit2.3wn;v lgbx zt7fst/tf,ij )h 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 morning jog on the dec 0po73cahyct9p* pj 4ek of a cruise ship is running toward the bow (front) of the ship at 2.2 c *joet0pph4y9 c 73pa$\mathrm{~m} / \mathrm{s}$ 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 0.1d hpmz: spfq-tt ,0v7edmp3 760$ \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 atlh )n(wnq1mcq mb- w0* qz)we() bq4dd 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 2.32zhxhpg-e6d:5sdb(w10e* do 8w ynng0$ \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 and vjnqyg5f-b2 60iz9 fig4x8j1 shomr9they spot each other when they are initially 11.0 k gmbf x1 4sz njf-2o6hg9 i8j9vi05qrym apart. How much time do the pilots have to take evasive action?    s

  An airplane is heading due south ise b3l23c*.3jy m g-nm i1e5q*tdr nrat 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 Problem 41 so i s*m,lsqmu+8 that it will fly due south? qu,l+ mms8i*s    $^{\circ} $ east of south

  Determine the speed of the boat with respect to t :3zp8ffn ; 3geez+wwhhe shore in Example 3–11.   

  A passenger on a boat movi6g1b d.7gg:xh p3n uikng 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 is 2.6 6 ( 1)hr*fb9 x.fjdwqxuvwhy(0 $\mathrm{~m} / \mathrm{s}$ 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 w9a9 qzbgkf 1+ 5kw4x ihl8fy19s4iwlcater 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 swimming zc+t;dss)*zjioq 6+3 htj: o;) kjhqz0.45 $\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 swf7.xi 9di xc 39deolus.:p*j dimming 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 svpr57rrzoxt *y:a *1 speed 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,j glzu,j):c7 v traveling 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 the spel31nl ai m8her/7kztf9m:x t.eder’s speed is not known. If the police car accelerates uniformly as given above, and overtakes the speedl i/7.re9xh3mft8m1za l n :tker after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner at hebg8w,a xqj 9oqr;3b *me+ t,right angles to each other (Fig. below). Car 1 travels at a speed re m;9b*xoh ,,q3je8t+ rwagb eqlative 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 sp tv89vs)w 8kp3sw6lyvlit the apple atop his son's head from a distance of 27 m . Whyvp6v tws k8v 38ws9)len 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 speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25 m south, /qs5bfu o8sdv (8pfl x*vz. :n;v1laeand 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 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. Assus/opldvb*f1f 5:a8;e zlx(v.q8s n vume 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, u(*he3xu4 le3 +lcqbx escape routes are sometimes placed to the side of the road for trucks whose brakes mighcuh lx 3 l(+*4ubex3eqt fail. 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) whose magnitude iv5jds bfk 7q) mr5x;k+ yuc+.5joga5vs 88.5 and b5xod+vj fyu.; )5 vmk+j5 sqg7 5krcawhose x component 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 6s2 vubo6zfj/$\theta=30^{\circ}$ 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 (h.s fdtkd .5 ;,)riol-y8fdbcg myh0 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 eu0xa6 g( od82rw;wbq* kn)a,r4eezv $\mathrm{~km} / \mathrm{h}$ 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 capaqa jyf8vb36+imr n hk**r9dk)ble of jumping 8.0 m . Assuming his horizontal speed is k qahj)9kr6mb8 +dr y*v3if* n9.1 $\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 07 zv7p+mpv nnw(p ic-ball about 180 m! Assuming that the swing, launch angle, and so on, were the same as on Earth where the +(p7n 0v nwpmp7c-izvsame 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 am69tw1d53h wn0 wo:igy vk-l7.5$-\mathrm{m}$ -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 plaf+spo p y;3 e6d1ovcunk*xs; 1tforms 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 clisp;1y fvx* pkn+1ouce od;6 s3ff 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 c8qpg//g :eaf4gwv.rhit the ball horizontally. What minimum speed is required for the barqg pfg./ 8ve/4:cawg ll to clear the 0.90-m-high net about 15.0 m from the server if the ball is “launched” 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, flyindh:o1 6 vjl7sd 2czyi6g a constant $215 \mathrm{~km} / \mathrm{h}$ 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 b x*x);y:r8pn0y w7 -jthl gywv . The boat is to make a round trip in a river whose current travels at speed u . Derive a formula for the time needed to make a round trip of total distance Dn8hr: y l) bwxxg*tyy0;p7wj- 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 t:uog,4rl, qgm o the top of a cliff which is 195 m away and 155 m high (see l, ugq4,g:omr
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 a. yfx9jx xgmyp)89g5 -ve.kk q3oz i:lt a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The player likes to shk 98mxvzi5j y-9l yoqk.)px:xgg.e f3oot 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 of amzhjlg)3d5/ ,igr -k1xzr;m(/bftd d $5.0-\mathrm{m}$ -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 carsvc2ufp k )+w7j / f1p :bn:5pixqg8cao parked side by side below a horizontal pu/fkg )wq17:p8ba ovc+x jp25 ic:nframp

(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 h44 bo09c wb9wxay1e m7yb qd0which leaves the bat 0.90 m above the ground at an angl0xwa41bqdwo9cy y m40be 9b7he of $61^{\circ}$ 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 s fwkucu n 13.j;d/m:jppeed 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 an initial velocity7jf66qap0*p nk1vxj h 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, any )mqowfz e wrd)-d/gs*w9+8kd being a clever physics student you decide to do a quick calculation to find its maximum hordwwkwdg)y+o/-e* )q8z fs r9m izontal range. You shoot 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?