One car travels due east at and a second cz s itt9a54l0e8vzycs ys71+car travels north at Are their velocities equal? Exsi15cz+ v7st0 c9a 8z4tyy sleplain.

Can you give several examples of an objech) j,uzxg(n+bt’s motion in which a great distance is traveled butbgn+ux( jhz ), the displacement is zero?

Can the displacement vector for a particle moving in two dimensions ever be longqieueda7/ks1 v ov6 z3-ha7-cer than the length of path traveled by the particled vh36 qzv1k sia7ou/a-e7c-e 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 lenmi3p,jo0ocpa u u2*86g(e dgg gth $ 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 thecq;o)c jy. q *rx64br1lk tnq. zero vector? Can three unequal vectors? Under what conditio 64cq l;trxq*cb 1..k)noyrjqns?

Can the magnitude of a vef)5nz p5m2 s/cy cix1pctor ever (a) be equal to one of its components, or (b) be l/p nmfsi x515)2 pczycess 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 on680ph2t7 w2.m) ezb*ld e yhleoves+ wto a moving walkway and then onto theb6ez ehy08.h+om7lp2)e t d2swlv ew* cars themselves. Why is this done?

If you are riding on a train that speeds p 5owqgz75xc- qrnr.6v ast another train moving in the same direction on an adjacent track, icq-o675x .5zr qrngvw t appears that the other train is moving backward. Why?

If you stand motionle hbt 96akgsr8.zv;-ec ss under an umbrella in a rainstorm where the drops fall vertically, you remain relatively dry. However, if you start running, the rain begins to hit 96-bshz e.8 rcagtkv;your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, movi c d04qmwvne 60dnzh6*ng at constant velocity, throws a ball straight up into the air end6qcn0zh4dmw 6 *v 0in 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 sam1 9e6xk :m2o8wz1skyw ue*z )jbhuo)ye 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 point. Which rower reaches theouyz21 z6uw)k)w: y9ho e ekxs *1jmb8 opposite side first? ----待选择----AB 

How do you think a baseball m1t*s q 9t31blhv xg-tplayer “judges” the flight of a fly ball? Which equation in this Chapter becomes part of the ptm-19*txv3s bltgh q1 layer’s intuition?

In archery, should the arrow be aimed directly at the target? How shofr aaw786 bgri+g-il1uld your angle of aim l+gf8wa7 ri1g ab6i-rdepend on the distance to the target?

  A projectile is launched at an angle hyp f,l :a;dug2d /h+fof $30^{\circ}$ 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 wit.qhq-4qa hc0wem w1rt64l mj ,h identical initial speeds,q1 r-6jmm q4.0qewta,wlh c4h but 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 km southwe ,axf+3lk4thu v.pzh65/ jemhst. What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagr hxt+p5hu, 3e4 6k/a zfmvlj.ham.

  A delivery truck travels 1kn6df p/4i.j ala(/ vx8 blocks north, 10 blocks east, and 16 blocks south. What is its final displacement from the origin? Assume the blocks are equal len6fpjk/a(d xvan .4/l igth.    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 r n,.ly55mabneun+ 3a uesultant of the following three vector displacements: (1) n+,ya.amue3n5b ln5u $ 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 vector t848flz cu7qx $\overrightarrow{\mathbf{V}}$ 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 travelingaktp ,+q 5rw*izay .-(j v(dxbss37cpudo;,a $735 \mathrm{~km} / \mathrm{h}$ 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.v0sxw9p r5 ag;)cm0 cy below. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with th)g a vcx09ycrs05m wp;e 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 +6 gs5q p1t t:)cjke3zuyvf2 e$ \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 abo s p+(bj y:mxf5*y: mrc-z9bkeve base camp, is measured on a map to be 4580 m horizontally from the camp in a direkjr-xpe:+ 9c*b5:f( mbmsyz y ction $32.5^{\circ}$ 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 pla ttvyj6wr 3lg 9pp :kb8**fl+mevzf83ne that has a magnitude of 70.0 units and a y component of What are the two possibilities fp v+t:9*3y jb*t f3lve l8wrm6 zkp8fgor its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a speed of How fa aiz/; drg)i4ygppe: +0+e t, s4svxycr from the bast; gir) ixd+p +es4vace 0,yz:gy4s/ pe of the rock will she land?    m

  A diver running dives out horizontally from the edge of a vertical ccm l8nct0 l-c m;tm90jliff and 3.0 s later reaches the water below. How high was the cliff, and how far fromc nmm009cjtl-t8 lc;m 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 k0g s bmr8in:1a speed of At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there two diffe0sr:gnmik 8b1 rent angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s winas4i *(sf : hmlzx;b59aeonl) dow, and he wants the pebbles to hit the window with:sa(;*blns4laof5h )miex z9 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 they hit her window?    m/s

  A ball is thrown horizontally from the roof of a building 45.zlnvm)rq2; ka h78a6 w9pbnx6 8l kqz30 m tall and lands 24.0 m from the base. What wzwrp6q9m2n kza k3b87)hnl6 x;l8qva as the ball’s initial speed?   

  A football is kicked at ground level wit4fjyhu l-a 3y-h 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 horizontalnl6b:kj*,bw .izth, b ly at from the roof of a building lands 36.0 m from the base of the *:h6z bw,lk .btbnj, ibuilding. How tall is the building?    m

  An athlete executing a long jump leaves the groudbi0md o v.q;1pby1e.+*9iin w w ng .b3iyee-nd 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 Moon as compared to tgmi/wr4qnr a m., f0)at,7scuhe Earth if the takeoff speed and angle are t)t m7/.mr sac,4 g0rfaqn iw,uhe same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a ta pf9e5h)rpah 49q x.7kbtew0y rget (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 traveling wants to drop supplies to flood tvai0)99 gi7rwh8 u gevictims isolated on a patch of land 160 m below. The supplies shoulvhg ug9)7 8tawer0i9 id 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 inithv iocl cjbj3 o+e5,8k9b10 s3uleo)nial speed of 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 cls+ gfq/s0ov1 siff 125 m above ground level with an initiofv1ss0/qg s+al 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 shot with an initial speed of 15z,0e ng .kv,el.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 proq a12bv82leu w4oe,ols fs89 bjectile equal its maximum height?fb12 9eoau l8 s l4svb8wo,q2e    ${\circ}$

Revisit Conceptual Example 3-7, a)5 or+fyt;bw lb,-hjf:q(lf and assume that the 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 trebrlt o(wj,5 l)- yqhffbf:+;ae makes the wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants to drop supplies to isolated mountain climbers on zp ,sfnr4*w kqkk( 2ki0 -hfw+a rocky ridge 23rifq 4, 0k2fk-hz(kk*w pnsw+5 m below. If the plane is traveling horizontally 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 morning jog on the debg+* +mipth k 9c,li49ipb *1)dhriebck of a cruise ship is running toward the bow (front) of tphe9)*9bp d+m+i 4h*gbciibrl1k i, 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 0.6w2z p:z (0-f v/i of,k/z/xe qfqc(mif0$ \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/ qg i01fnwt*x 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 2.30 qg-7up(z /*f/5ce gf 8oqkphe$ \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-op*lk*b*i y9xk n. Each has a speed of and they spot each otherli9**bpk yx*k when they are initially 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is heading due soutag( 9m8i oa-il7+b gvxh 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 Problem 41 so that it wilj4j 2g /rjwvt.5msxa ;l fly due 2w sjm4av5; r.jx t/gjsouth?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shoruzbl)y)biz, k,+/ dhe e in Example 3–11.   

  A passenger on a boab n6*kajfo(-fc f)d2q t 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 speepq9 q3+he3ao c(kuv 4gd in still 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 sun7j o8 o0fi5pm ph6c;aq:mn( till 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 capablem*qoz). sh9q4 v me u6)1ggstz of swimming 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 swivpyc+zj2t /,zobi;) mmming 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 is 620lk*j5 v(f0 0r4gfdsm0 ay 1vly$ \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, travel8ed.mxi cs9g+si.vici)g bm(uf 62 a0 pui;y+ing 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 speeder’s speed is not known6n*dmg mkpt86 d)o gh9. If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was the speeder’s s )h9t d*kd6opnggmm 86peed?    km/h

  Two cars approach a streedtz 7/6aex mz0 +a6jra4j5r84u sevji t corner at right angles to each other (Fig. below). Car 1 traveljae + iua7r654s6 td/jz j m0av8ez4rxs 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 the apple atop his son's head from a distance o3b kcg9kzfc7c( my +l8f 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aim3cg c 8c k9lbfzy(km+7 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, war plqs.g43:qglks 50 m east and 25 m south, 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 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, grls 4q:.qgp3y 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 plov fi/1 - ooy(twwo7;laced to the side of the road for trucks whose brakes might failfy/w-;(wooi 7o1lt vo. 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 pl9z*7ofu*u z u,:jg jsgane) whose magnitude is 88.5 and whose x ,ujz u: g7jguszo **f9 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 .i9r(han8*p3 boe,e wc 1ug oojg1m-o $\theta=30^{\circ}$ 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 1a m)kog( tgb,6j8hyldue 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 zs m6,zy7cid*$\mathrm{~km} / \mathrm{h}$ 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 . Assuming his horizo2i+2 x8wsvfbp ntal speed is 9bxv +psw8f22 i.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 irovlwy sp c4; enk)8 (h:m5ef8con” to the Moon and hit a golf ball about 180 m! Assuming that the 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 fme48k()oln5s pew cyv: c8 ;hin both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a pqwk*91wk l.u tf*2dvpi h 8i/5iebb5homer over 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 Acapulco push off horizontally from rock platforms about gi0x3.n.3 d7zs 8 f lsey s34wv*uqasf35 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 d.*l.373qufa x30 wgfs sez s8i4nysdvirectly 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 horiztohki6b lh* 5(ontally. 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 “b(ihlo *5 tk6hlaunched” 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, flyingkvhxa6z yhbi :v 8qb 9,0)4z(z ywsh:j 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 v . The boat is to makei40gaaoq w3buo, 6a g/ a round trip in a river whose current travels at speed u . Derive a formula for the time needed to m,o aqu/wbi a0og34ga 6ake 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 gro k6opuytt6++d6nz*y m und level to the top of a cliff which is 195 m awan6zmt*6oy+td6 +uk pyy and 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 qv:+6a5w ig0v/1l jljxek pe5 height of 2.10 m above the floor. The basket is 2.60 m above the floor. Th0gq+6 ai pvwlv:1e j/k 5xjl5ee 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 thec0v)qfy3)x bf 9m7 dmc 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 hqut)* ce kpz4:c*3e kd:ne 7mcar jump over eight cars parked side by side below a horizontal r):cm3qhe ect:k*npu k* e d4z7amp

(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 aboi-ih;ay814d3jp ma rove the ground at an angle of i1j3-ry i;8aa 4 podmh$61^{\circ}$ 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 of )obf belk*b - o9e:t*g $32 \mathrm{~m} / \mathrm{s}$ 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*1z /evbk* tw;htf2uid ./fif top of a building with 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 s/ov,gj8z xu62cu,.nqm 6(r s iftwel6tudent you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straicuitx6wu fqgsojl.,m6ern v862(/ z,ght 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?