One car travels due east at and a second car travels nort) *bgx*n z c,ad(j8kixh at Are their velocities equal? Expz8n )cd*b ix*g,ax(jklain.

Can you give several examples of an object k3uxcd.-0bmx’s motion in which a great distance is -d.x 03mcbkx utraveled but the displacement is zero?

Can the displacement vector for a particle moving in two dimensions ever be lsz4 b8uq5u+j q6499 ju qnltl8jg,zywonger than the length of path traveled by the particle over the same time interval? Cajl5,n+byq 9 wsgz6t lu89u zjqu 484qjn 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 qs 5 q, ul/kium+k(z9l$ 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 unequa/j/zkt bv) n pk*d-n-3 p+lntfl magnitude add up to give the zero vector? Can three ubljvppk/ +3 n) t *t/--zfndknnequal vectors? Under what conditions?

Can the magnitude of a vector ever (a) prr7ii(;)sip 5 uaztf-w f 39ybe equal to one of its components, or (b) be less than one of its compo7;rf5spz-)puia93w i ftry( inents?

  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, g/ /ro4gv p4. g/ljzdcto get on a moving “car” the riders first hop onto a moving walkway and then onto the cars r/lzcgg/4jo/d v4g.pthemselves. Why is this done?

If you are riding on a train that speeds past wxc,*pf bh (/mvt6,dsanother train moving in the same directif tb*hsv/c p(6,dwmx,on on an adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under an umbrella in a rainstorm where the drops if6-:d)inn m8 xw//igu.iz 4tcogan7a.nz7zfall vertically, you remain rela/ nw7.-.c iii)ugza4 ian8onznm 6xtdf gz7:/tively dry. However, if you start running, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at constaiskvy:xo /jc4sw2.i1j)p o,gnt velocity, throws a bas24): 1v ijpogx .oy/wi,sjkcll straight up into the air in her reference frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row ao86rok 8i*cm vd7x83 tr8yyrn t the same 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 6 d8x3 *8yt rrrokcv8m8 yo7nithe starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a basebasj.mzg4(b3s jll player “judges” the flight of a fly ball? Which equation in this Ch.3 (jzg jbms4sapter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the target? How should yourf8ryy*9 urkmbq +7x/: rnx+su angle of+rb rxxyf7 q/u8+*nr : mysuk9 aim depend on the distance to the target?

  A projectile is launched at an anpw7 bywywa 2.3gle 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 g:i tdlog ;k7 i4p0m7jyround with identical initial speedsi o7gimt7 jlk d;0p:y4, 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 thenwr9p8 d)z lwj ;5ar2dd 85 km southwest. What is the displacement of the carw;)dlpr98dj2a z 5rdw from the point of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, c/33rst akg7v0c*cwcm*h 0fn10 blocks east, and 16 blocks south. What is its final displacements**3n kfwc3vm0g0 h7 ct/ ccar from the origin? Assume the blocks are equal length.    blocks

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

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

Graphically determine the resultant of the ojy qtuf.1 k6hw-* ,msfollowing three vector displacements:1 u-s,h. 6mfkyqt*woj (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 vector ruopjl o gdr9 ,es;/86:yg d,s $\overrightarrow{\mathbf{V}}$ 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)0s4zskdc g* v $735 \mathrm{~km} / \mathrm{h}$ 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 showb s *gwvfkt1lnp 8gwj mz,y6,oo +;0l)n in Fig. below. Their magnitudes are given in arbitrary units. Deter,0t o6f)*lkv wlz8wms1,;+p gjgbo nymine 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 rgn:)e w:t:bh cvqf tej3 , q,da)tyq/f.74pz$ \overrightarrow{\mathbf{A}}$ and $ \overrightarrow{\mathbf{B}}$ shown in Fig. below , determine $\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}$ . (b) Determine $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}$ without using your answer in (a) . Then compare your results and see if they are opposite.


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

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




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

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



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

  The summit of a mountain, 2450 m above base camp, is measured on a xjix4s)s x,2smap to be 4580 m horizontally from the camp in a si2sjxx 4)x s,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 ad.44bpt.g j/ :bo9p jn1v0ftcw y;hal* og9aznd a y component of Wy;g9 j d/:t zv tb*w9jl0. .n hap4cfbaoo41pghat are the two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-hig 8k3wv;n84zm-y prkaeh rock with a speed of How far from the y88za npe;rm k-w43vkbase of the rock will she land?    m

  A diver running dives out h 3g+j gn,0thu(wm+ 4je.b:rn8iackaa orizontally from the edge of a vertical cliff and 3.0 s later recjeart ,jb(w .8g + ig3amkuna n:40+haches the water below. How high was the cliff, and how far from its base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground i hqbdvbzv2 94;54nxl 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? Sket4nhdv9i5x zlbv4q ;b 2ch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, and he wants the pe84w:)h hwqmagpx ,x4-z dpwq0bbles to hit the window with only a horizontal component of velocity. He is standing w -:z0qhw8gpmd)wxahxp q44 , 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 tal)5f 1r hdsq8bxpbm 2;cl and lands 24.0 m from th2bb5;hcr m1qxfdp 8)s e base. What was the ball’s initial speed?   

  A football is kicked at grou+tabwnwn/ (s o l6j;31rc*o8emsd8f*ee wv2 tnd 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 x .wfd7,i7fd.emqpk/ lands 36.0 m from the base of the building. How tall id7q,kfpd/ x.f7e.w ims the building?    m

  An athlete executing a long jump leaves the groa( xae y1 t*-n)/ uh8+elmgpawam ;hp5und 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,4 4ffitf ye8mp.wop:* gmi-m the Earth if the takeoff speed and angle are t*m fyp.:gmt4ii 4wop- e,8mff he same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 75.0 m away.z y50*71l qefpdj5puf
(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 supplih/qh fbh1 .bkhi* hd4;es to flood victims isolated on a bkhbfhi/*. hqh dh1;4patch 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 initialtg(00ca6 lw-j gcpn(er c6ve; 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 edf9v)kf5sljoc, em:6;g1qvh+skq5y y ge of a cliff 125 m above ground level with an initial speed of at an angle of 37.0º with the horizontal, as shown in Fig. be, :mq5k;cks9v6f )y lqeh jsoyvfg15+low.
(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 15.50rrtov9l dxvwr,4r3 e3 zoz58 $\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 equal its m hj3ue 4qkjg q5s(h6.vaximum height(5u4q3vh g jsejhkq6.?    ${\circ}$

Revisit Conceptual Exampxe ;o.(5fx, j:(a/mzjvp7rgz 6sts qule 3-7, and assume that the boy with the slingshot is below the boy in the tree (Fig./r z, ( sza5gqemjfvpo:u6jxst(; x7. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants to drop supplies to isolated mountch-5pi;.2 d v9szxake(ga bk0 ain climbers on a rocky ridge 235 m below. If the plane is traveling horizoh;gap0vxs 9.eazdkc b i5(-k2ntally 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 c+us.xpd2vhs-l+ (k 9)x4br xxqh,plu ruise ship is running toward the bow (front) of the shhlvs, x-)+plx4(xuq .u9 +r kp x2bhdsip 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 q9puw:2d co.b zvkyl0h24 7bb8 bntt10.60$ \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 on wep*(uo: ng ziy,(u +0t+gqkza 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 2.30ng nv23/pp dw63)mj6axm5o hr$ \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. w gfdokza ;z;ys-r1 .3Each has a speed of and they spot each other;;rg zy .zdk- 1a3wsfo 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 south at a speed of a hzh9m yma:f0 2vyv00600$ \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 pilcr8 mzo1yc j(,ot aim the plane in Problem 41 so that it will fly due south? ycco8 zjr( ,1m   $^{\circ} $ east of south

  Determine the speed of the bo,e cus92gtijd )5 u-7oz8pe vrat with respect to the shore in Example 3–11.   

  A passenger on a boat moving at 1.5t r;0ijkbv:sufopqg (e:if *;2vt1:b0$ \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 sp6)2n+ 6d-vhhpixqme) ik7c y seed 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 6y. wv0lzb- pe.ba 46kdfa*phstill 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 swimmi7.d8le ad1mu1.glexj ng 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 0.45 0gy2jrcrs)8r$\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 byq 5 s8udblk+;st;k1 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 ca n j/l a f55 8i2)iwta:1.7jviqstszhsr, 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 speeder’s speedb+vzl6d:sw(0 yhpk sa6lis.4 is not known. If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, 4 6ass+60wyipkvl dzb.s:(lhwhat was the speeder’s speed?    km/h

  Two cars approach a street corner at right angles to each other (Fig. benj xra* 6c3y85hlc5 uvt(7q pnlow). Car 1 travels at a speed relative ur l55nx8c *nqv7 yj (36hatcpto 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 apjxx8uut +;lm.ple 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 tx+ju;.l8 x umhe 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 tru ::at2 gpr.qph s1s,z:pxeb+jx+zq hor+2tj:ck, walks 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 ej q b,hpz22h:+.e:zj+x:ppg ar+rsox1tt: s qast, 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 ro,vr( kka/*/*h7bblqp-mp vjj ads, escape routes are sometimes placed to the side of the road fop j*b- v7lpjk/,bkm(rv/hq* ar trucks whose brakes 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 vector (in the x y plane) whose magnitude is 88jc-kc48xyw b8.5 and whose x componeyxc w 4c8jkb8-nt 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 anglhvl vmy; . waeuvmp53-r. /ua2e $\theta=30^{\circ}$ with the vertical when viewed through a moving train window (Fig. below). If the speed of the train is $20 \; m/s$ (a) what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically?    $m/s$
(b) what is the speed of the raindrops relative to the train?    $m/s$

  A light plane is headed due south with a*z s xf/o/9l1g fs bo3qteu:0v,etx)v 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 * y5)pz wjm1a7wczo x8$\mathrm{~km} / \mathrm{h}$ 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 . Assumivv1li.8jma ij :e ;vt9ng his horizontal speed is 9.1 tj ievvi;.v ja:m189l $\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 too4g. :xfhg7g)):l3gjpsfh 0 cmt5q juwk a “nine iron” 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 i)qhg)sgcfx : 4f.tpgmwu hj7l3:jg05n both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer9m( uk5yua q2k 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 horizou ws6 xv.s.05wgbwod*ntally 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 pu 6*owvs.b w0s.d w5gxoint. 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 bal0 kzrdln* /x(8sa.p evl horizontally. What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is “launched” from a hei(vl*rxz8e0.p ds/ an kght 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, flyin ;tqm-y 1rs*fzy +wcc;g 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 make a round trip in lr vdy jxrf412x83ej9g2a5mc a river whose current travels at speed u . Derive a formula for the time needed2f49vxm23xr1rj jad eg 5cy l8 to make a round trip of total distance D if the boat makes the round trip by moving (a) upstream and back downstream, (b) directly across the river and back. We must assume u

  A projectile is launched from ground level to the top of a c kz-,mlx4(bwr -iwsu *liff which is 195 m away akbr,zx- ils(w m*u w-4nd 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 sqx uu 2+pbfmr( /li1q3n(-zxa height of 2.10 m above the floor. The basket is 2.60 m above the floor. Th+ /1xfqibs p2u(rlmq -uzn(3xe 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 theh:zhcq n6,-ddxx45 z- /4 h3fbepx uzh end of a $5.0-\mathrm{m}$ -high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine
( a ) her initial velocity, $ \overrightarrow{\mathbf{v}}_{0}$ ,    ${ }^{\circ} \text { above the horizontal }$
(b) the maximum height reached,   
(c) the velocity $ \overrightarrow{\mathbf{v}}_{\mathrm{f}}$ with which she enters the water.    $^{\circ} $ $\text { (below the horizontal) }$

  A stunt driver wants to make his car jump o+,z0a n9 8v2gcd7sym,gu ids h:1mmfover eight cars parked side by side below aysz9 fh +uga:igvdmmcn8ds, 1om2,70 horizontal ramp

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

  A batter hits a fly ball which leaves the bat 0.90 m above the grouny wykez * g7sxh7z8u4/d at an angle of 8u sxe /z*ghyzy47w7k$61^{\circ}$ 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 b6k9a/e oq+ : nrg)kvivaseball with 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 g7avwo8 (ze 53(qtsim 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 student you decide to.tdhlx4 k4g2 jk0 )6zwj/hm wl do a quick calculation to find its maximum horizontal 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 y 0lh x4 t kwg4.j/hw2l6kmjzd)our gun?