One car travels due east at acp 3gtu82:9h4pes) vc:bgkhh slw/. rnd a second car travels north at Are their veloce:pschg gpr 89b/sh3t v .c:kuhl42w)ities equal? Explain.

Can you give several examples of an object’s motion in which 5q8a g1cjrva1c 73ffb a great distance is traveled but the displacc8 3qbag7f11jfc 5avrement is zero?

Can the displacement vector for a particle moving in two dimensions ever b 1e( 3 n+d.l.ekfuyc.y/kqguoe longer than the length of path traveled by the partikuok.g1/e .+uy. (d nql3ycfe cle 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 lengb 2t/xcu;diyma/ ,c 6uth $ 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 th6umig6q*o t uqyp. ru v/c23r+e zero vector? Can three unequal.626y 3 qr/ iruot+ugmc*qvpu vectors? Under what conditions?

Can the magnitude of a vector ever (a) be equal to lk 9bs+8tzcn5. 2 mqnwzf5 m6cone of its components, or (b) be less than one o6cfkm9+2 zscw5t8bnnz 5.m lq f 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 jtw9pb;0hzi(9x i(n tget on a moving “car” the riders first hop onto a moving walkp0 9n9;w txjtz(h(i biway and then onto the cars themselves. Why is this done?

If you are riding on a train that speeds p 5iw;+qg p8pxiast another train moving in the same direction on an adjacent track, it appears that the other train g5 xp;q8+piiwis moving backward. Why?

If you stand motionles6b9 fi 1 e0xjjo2mfi-94petim s 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 your legs even ibximofe m9ej1-fp 2i0tj 694 if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at constant velocitykryij cf3yo q1q /wl5ps31/l;, throws a ball straight up into t/jq5y13 / s3qyi1pcf;rl wkolhe 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 v .yu /glznrb-q*lq:e 7jqd:0 row at the same speed in still water, set off across a river at the same time. A 0bgvlr.n: y/qu7-d lj:e*zqq 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 the opposite side first? ----待选择----AB 

How do you think a basku w5;8x + p5w6xguopvt.c)areball player “judges” the flight of a fly ball? Which equation in tuxuc) o5 a p5.r;kw tx6w8gv+phis Chapter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly 8e*r*zzbjn w9 at the target? How should your angle of aim depend on the distance to the target?b n*z8ejzr9w*

  A projectile is launche+y;;nktv 2zgjd at 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 it-+4 x aapkj2ydentical initial speeds, butp- ay4jx+t 2ak 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 southwes+ 9e; s1vh) gwrpgt1dat. What is the displacement of the car from the point of origin (magnitude and direction)? Draw+p;dvha1s )er91gg tw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and4gnw m9q a3e:*bj s+1rgmdt7x 16 blocks south. What is its final displacement from the origin? Assume the blockm 3t4 wd+nr:9xe 1sg*j7ag mqbs 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 resultgcbeny wtz9 gx9/.( 6bm/: s+gyrdph*ant of the following three vector displacements: .9:cdtxwmbsy*z6gghbgn/ epr +9/y((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 vemch2s ))x1m9e if 8jtvctor $\overrightarrow{\mathbf{V}}$ 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 travenuj0ga 9 q56baling $735 \mathrm{~km} / \mathrm{h}$ 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. Theirq-dsz8mc o,wro:oy(+ i0fdz*d3 x -wk magnitudes are given in arbitrary units. Determine trwd xymw+q* -kd3 -o dscz i(o:,8z0fohe 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 urldt7nh*zy 0 ppu)8-t 7b5zt $ \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 eu9 whp 7kpt7+r/qv b2measured on a map to be 4580 m horizon utbh+qr9e w/v2p7 7pktally from the camp in a direction $32.5^{\circ}$ west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north, and z axis up. x =    y =    $|\overrightarrow{\mathbf{r}}|$ =   

  You are given a vector in the xy plane that has a magnitude of 70.0 units a2, y9xinc oq0lmqzm49v 6bzc(nd a y component of What are the two possiqqym,on62z (z 90 m cv94xicblbilities for its x component? x = $\pm$   

  A tiger leaps horizontally fwb 2py eh/vi9)rom a 6.5-m-high rock with a speed of How far from the base of the rock vw b9p/ehy) i2will she land?    m

  A diver running dives out horizontally from the edgeehl :.l kx5xw5nxq-+ d of a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its b-hn .x:ewq k5l l5d+xxase did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the )t2a: jbz rl)3 n7amtpground shoots water at a 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 different angles? Sketch the two trajt apr7n)b)mz3l ajt: 2ectories.

  Romeo is chucking pebbles gently up to Juliet’s window, and he wanzr 9p 7vt*ik:2pya )gjts the pebbles to hit th ptg i)z7av:y k29*jrpe 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 they hit her window?    m/s

  A ball is thrown horizontally from the roof of a building 45.0 m tall r*/ibz pftmj j q. 2tc70czbtvh:06;vand lands 24.0 m from the base. What was the ball’s initial speed? hvi0t2:q70p r bb6cjm;ft*v zt /zcj.  

  A football is kicked at gc(eo/,gvkj(z3rl -ir round level with 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 land4 e em+c(glot:4y;iv0vc6 v,mj.ll avs 36.0 m from the base of the buildi4:lagecvmotvi ;e6vl (y4c. 0vm jl+, ng. How tall is the building?    m

  An athlete executing a long jump leaves the ground , s*d mmpm8wzrwu v(ksvy-5 ,:o/.thj 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 comparedp*my4bz b3x 7u to the Earth if the takeoff speed and angle ar*b37b yxm u4zpe the same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims direct(tcn t;3a4gjfkw0f 6m +edi,e+y2p vcly at a target (on the same level) 75.0 m away.
(a) If the bullet leaves the gun at a speed of by how much will it miss the target?  
(b) At what angle should the gun be aimed so as to hit the target?    $^{\circ}$

  The pilot of an airplane traveling wantp(je j r:ny,v6679wwxrv4nd qs to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly or9y6r4n vv:x wd7j(pe6w qj,nverhead?    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 io o9teyx 5mznq:i3n /m)4 o9oof 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 t+lp13ux-) hanzlf:q dg5t4b cliff 125 m above ground level with an initial speed of at an angle of 37.0º with the horizontal, as shown in Fiztatn+4 ud3l-bq1 l :h5g)p fxg. 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 /749im ffnkip56lo lp$\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 rangef:3y ykw:6h2to e3 lpx of a projectile equal its maximum height? 3 :eytfwy2xo h6pk:l3    ${\circ}$

Revisit Conceptual Example 3-7,yl2jrzk1q)a zk+a bv 3:3xg7 q 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 tree makes the wrong move by letting go at the yx)qa 2l7 vk1: az3qrg+3kzjb moment the water balloon is shot.

  A rescue plane wants to dropbwrm2imv05nbt f) ww.8 a4y.mgrr; oa:82qe v supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling w0 rwa2vb;grma r 5.v 4:m)8.mw28ie qbtonfyhorizontally 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 deck of a cruise ship is runni wq*gylizu*9ozk-cx3 ;w4; qjng toward the bow ;q *qjwk 3 yix; -g4uzzclow*9(front) of the ship at 2.2 $\mathrm{~m} / \mathrm{s}$ while the ship is moving ahead at 7.5 $\mathrm{~m} / \mathrm{s}$ . What is the velocity of the jogger relative to the water?    m/s
Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?    m/s

  Huck Finn walks at a speed of+n 72;l(9 eswsr nljth 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 orhgpap ns)yp/ip,pvt+do8(pk,f*, : n 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 2.39 2,)y uqzztgxp0 v.vy0$ \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 they spot eacm. sj:z0pd9fxfx n5v0h other when thepns9 z.0 ffmx:50dxvjy are initially 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is heading d)y : r 2q2r:k:f ogvfh4xdgf4gue 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 Problem 41 so that it wuxppo(tb 65zy.+kx) nill fbt p+n(oykx p)5 6uxz.ly due south?    $^{\circ} $ east of south

  Determine the speed of the boat with pkxk;xcn56i;xcnzs v,qpf69i:d 0yf 78x0 vhrespect to the shore in Example 3–11.   

  A passenger on a boat m;t rj w3r2-om1k4p. v97qdq u*ccowy doving 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 2.60 we a7fi:g9r6 d$\mathrm{~m} / \mathrm{s}$ 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 iwxx5h2wlhm hzn,,.z8j a .bh 6n still water is 1.70 $\mathrm{~m} / \mathrm{s} $, must cross a $260-\mathrm{m}$ -wide river and arrive at a point 110 m upstream from where it starts (Fig. below). To do so, the pilot must head the boat at a 45$^{\circ}$ upstream angle.


What is the speed of the river's current?   

  A swimmer is capable of swim,4 dop ycqt5ext il k)z(-mg3fak9 *t3ming 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 09(o gb3eankd2 .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 1q zcrq d4iyv;007 b d1ukws4pis 620$ \mathrm{~km} / \mathrm{h}$ is supposed to fly in a straight path 35.0$^{\circ}$ north of east. But a steady 95$ \mathrm{~km} / \mathrm{h} $ wind is blowing from the north. In what direction should the plane head?    $^{\circ} $ north of east

  An unmarked police car, traveling ag,0+ kki4lvajg r. kqhwl+/k 1 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 tho o o9o7kf y2hg; i6.-lj:dlvqkw9.fjat the speeder’s speed is not known. If the police car accelerates uniformly as given abovio2 g9 jkdv7.6y:whq.oko -lfj9ofl;e, and overtakes the speeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street coy5 ozv.p26 z rnrnna)8/x-,m vl yze3orner at right angles to each other (Fig. below). Car 1 tr)vzn l ex3az.,oyny5o2 mnv/rr z-86pavels 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 thvi*fs1s2w3k/.itdwec h/ s 4b 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 aiv.2h*f/kc bt/ wissd3esi4 1 wm 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, p7bnfxat- 6z ns;8x/owalks 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. Wx6-sx8oz/tn b;a7 pf nhat is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

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

  On mountainous downhill roads, escape routes are sometimes placed to the sid apm9xq 35wtjwnq 2ws(/m(i)de of the road for trucks whose brakep2dq/wm wmxtaq 9(s( ji5n )w3s might 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 v ,n2wpx -lq qgyg*c7b+ector (in the x y plane) whose magnitude is 88.5 and whose x compo, 7cp2x*ql-bgw y+qng nent 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 ang2mkaruq5mj8/ ol;v+iny cq /3 le $\theta=30^{\circ}$ 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 .j:kqtq9 8jxl b2h1z7:gqox fwith 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 +la,du z3e),ipcxn4p$\mathrm{~km} / \mathrm{h}$ 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 horizontal 4+o5ly9+s 1bkv4t ojxo .)dos.hf cq zspelyqo5c +) f+4h9x1kvztdo j4..ossbo ed is 9.1 $\mathrm{~m} / \mathrm{s} $ as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright - that is, the same way he left the ground. t =    y =   

  Apollo astronauts took a “nine iron” tos1ru i, kzpkfoc7c h-svndeq4, 0 7(+k the Moon and hit a golf ball about 180 m! Assuming that the swing, launch angle, and so on, were ccus+ s47rk-e vqk0z,hfkd o(n pi1, 7the same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over the 74g 9ppetlv9w9wejp// oi.*vc.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 pusv0k ,)5p*b surger.t mh 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 point. See Fig. below. What minimum pushoff speed isvrt0pgs ue .bmr,)*k5 necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizoz1o-8z /wjdkq ntally. What minimum speed is8 wzd/1o q-zjk required for the ball 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, flying a coydhpt;sb* dmd2 o3(o/nstant $215 \mathrm{~km} / \mathrm{h}$ 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 roue .mhdslhf ,db7 (/si.ah/ v(cnd 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 D if the boat makes the round trip by moving (a) upstream and back downstream, (b) directly across the s,admhcf.h / (.d(le vb/h s7iriver and back. We must assume u

  A projectile is launched from ground level to the top offo1 d1(a ogpc: a cliff which is 195 m away and 155 m high (of(cp1g: d1oa 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 4rmf:nqfp1njka4. 7b's hands at a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The player . 7npf44ab:rq1mf k jnlikes 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 ofysu*o8, fq r.l a $5.0-\mathrm{m}$ -high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine
( a ) her initial velocity, $ \overrightarrow{\mathbf{v}}_{0}$ ,    ${ }^{\circ} \text { above the horizontal }$
(b) the maximum height reached,   
(c) the velocity $ \overrightarrow{\mathbf{v}}_{\mathrm{f}}$ with which she enters the water.    $^{\circ} $ $\text { (below the horizontal) }$

  A stunt driver wants to make his car jump over ei4ajg8 m ::yu-kr /y w),sqajhsght cars parked side by side below a horizontal ram,:w 4sqy a y-kghua:r)/ jj8smp

(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 the9tc8/ yxue;qp ground at an angle ofqpe /u9tx8; yc $61^{\circ}$ 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 withx1 )zf f3w9iyo5zua4o an initial speed 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 witrm.8ev8h96p jh we7gk h 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 beinls: x vdlf.hoh. q+9j4hix5:jg a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the : l.:oxs4xjifh5 hl qhj.vd +9gun 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?