One car travels due east at and a second crlii 2mh:vd85+wh;c par travels north at Are their velocities equal? Explaiwc 5 lh;hv2m:rdiip+8n.

Can you give several examples of an obgn8s)1q + jfwcrz+em -ject’s motion in which a great distance is traveled but the displz81+jsw + )q rf-cnmgeacement is zero?

Can the displacement vector for a particle moving in tj0 hffai5a08hi,8sh2 tkdq/p(ikawm3 2n 5 qvwo dimensions ever be longer than the length of path traveled by the particle over the same time interval? Can it ever be les k h0fskfit 8(0dw n,8i 2 5h/haqiqvjm2ap53as? 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 len9l 1zd 62s .jhp,jpxzvgth $ 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 9ztf,r9 n xsol7:6 xluto give the zero vector? Can three unequal vectors? Under whx99ut6 r flz: 7xnlo,sat conditions?

Can the magnitude of a vector ever (a) be equal to one of its cl 1l ,ku3mea x1i*l5gdomponents, or (b)dll lk,g*mu xi135 ea1 be less than one of its components?

  Can a particle with constant speed be accelerating? ----待选择----YesNo  What if it has constant velocity? ----待选择----YesNo 

At some amusement parks, to get on a moviddua88rwa 0g2 ng “car” the riders first hop onto a moving walkway and then onto the cars themsd8au20 da8g wrelves. Why is this done?

If you are riding on a train that speeds past another tg9l b y9uhki f0vm be ey1(d: fr5yapd++)y/+qrain moving in the same dire/ (d p091fkeihdvyy f +rmgl+buq9)a5b:y +yection on an adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless un9u;(pmv9wcxe m*nz f.uh9dc*fy 0 pd2der 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 if they remain under the umb*fx 0dyc99h w2ucf*;edn9mp v.(pu mzrella. Why?

  A person sitting in an enclosed train car, moving at conx:;nvlbh1 o9e stant velocity, throws a ball strl1 9bh;o: enxvaight up into the air in her reference frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row at the same td(8la8j 3idrrm f5k8speed 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 t trki83 8jd5 frda(8mlo arrive at a point opposite the starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baseball play29zqg0*ti1nnv:k ms 1 mvd q9rer “judges” the flight of a fly ball? Which equation in this Chapter becomes part of rtvn1q0i:2v*zd9 g1nq9mm s kthe player’s intuition?

In archery, should the6y/s rgw ggtqn-;6e51 3 ,6zkl laxmoq arrow be aimed directly at the target? How should your angle of aim depend on the6e 6k- gomwnq;r 3sqlt1y lg5 /,6xagz distance to the target?

  A projectile is launched at an angle/p3: sz0hxqfx:b8 qf 9v0 upct 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 f/kc4lpa1 h a7+wrj4n.uy h5fxrom the ground with identical initial speeds, but wityh7a/5 lpn fhc.14jwkr+xa u4h $ \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 8( fc*hkq/y wh/5 km southwest. What is the displacement of the car from the point of origin (magnitude ank*wqhc /y h(f/d direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 1 hq*2 a6m5lgjqpt3ak 36 blocks south. What is its final displacement from the origin? Assume t3ak56pq2 mta l3qj*gh he 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 followin 0dd h),.+bvztyy) n(bt cjha8g three vector displacements:h d, 0ct.zb8(ybd +y))hjnavt (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 vecto1 0r3u xm:p z rq,f6r2lncfzv(aa (2xsr $\overrightarrow{\mathbf{V}}$ 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 lit5df uauc p72b/f,0$735 \mathrm{~km} / \mathrm{h}$ 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. 1qvgb96g u2e ca);jox Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Giux9o61 jv)gaq gb;c 2eve 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 vectorsgjkf (:*uwvp3 $ \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, 2*qecq+ns ywg*3 -i1h/ho8( l8kuzwr q450 m above base camp, is measured on a map to be 4580 m horizo18+3-snqkew wog hhu*cqlq r(z8i *y/ntally 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 70lry (n1 +qsx*y(47m idlh-g dg.0 units and a y component of What are the two possi g(ls+*rd4lyx7ni g y1d-m(hqbilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high gwb - .zmo-1ssp 2heh7rock with a speed of How far from the base of the rock wi-.hzm17ebs -g2shop w ll she land?    m

  A diver running dives out horizontally from the edge of a vertic*fvhnf27l,xi ;w/9 zf*y4kym /izwyk al cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from iwy yzif; nk7,2*m/z xwy /l9fhfivk4*ts base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water at a speed of At what angle(so)i h- m9oeco,) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there twic,m - o9)heooo different angles? Sketch the two trajectories.

  Romeo is chucking pebblespyk8o3+gjow:),cc ad gently up to Juliet’s window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the pek oojy, +w3p:dcacg)8bbles going when they hit her window?    m/s

  A ball is thrown horizont/qhlpis v;9ed+*2 2hu7t vjn t2ytn+rally from the roof of a building 45.0 m tall and lands 24.0 m from the base. tq9t+7sd;u/nelp t*j22 i2+hrv y nvhWhat was the ball’s initial speed?   

  A football is kicked at ground levelxtv mt/8mj-jck8m v9x, *uc/y 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 landsqvqkbkx8feop * /r/p03 8bzc, 36.0 m from the base of the building3 8 0ecpkkfx8o,*pz /qbqr/bv. How tall is the building?    m

  An athlete executing a lotlkfo-m/2ya8*p7-u j ez b)ezng jump leaves the ground 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 sc .7 4aef nton15/wijmk ha,2jump on the Moon as compared to the Earth if the takeoff speed and angle are the same,eik1/sw n5t 2 aja c7no4.mfh. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target gy-/ffj31ry * v ikfrs+b ,hv4(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 floo et10oug ,l5ag b9tus5d victims isolated on a patch of land 160 m besua5gtb o 09, teglu15low. The supplies should be dropped how many seconds before the plane is directly overhead?    s

Show that the speed with which a projectile leaves the ground is equal to its speed just before it strikes the ground at the end of its journey, assuming the firing level equals the landing level.

  A projectile is fired with an initial speed of at,xrr044 . exign i1w 2 36yds)wgvoskp 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 cliff 125 m above ground leve(*q ocu d:*s 4 ip r d7.svehu1nv/y.fvm*os7ll with an im(c.vq7vio ysse*/n s*fdolhr :u . dp *74vu1nitial 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 w .en;)fq yyw-with an initial speed of 15.5 $\mathrm{~m} / \mathrm{s} $ at a $ 34.0^{\circ}$ angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 m above the ground.   

  At what projection angle will the range of a projectih azdv +c3j;2r;jrzb)j7 l x)ble equal its maximum height?2l) vbzb+hzj j;adx7;r jcr)3    ${\circ}$

Revisit Conceptual Example 3-7, and as tjv c,w*jfn4g0g xs.+nzr/6x sume 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 /4xn* tnf0v wjz.ggs+j,x6r cthe wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants to drop supp5 bn;a+dcbai1ys x1 sp. tdg-3m.lpn0lies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with a speed of 25pb0p31dg1m5ys.xbdt c ; n+ia al-n s.0 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

(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 running toward rbc4 3o,p filnum a+p i0p5d4(the bo3+f dr,p 5mli nipup4(40b acow (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 sdtfwgpr*) ulzi( 2m9wc :,*a(c9i xnrx*.br 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 on a higa h cq5n,3f2:juoi 7iqhway 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 2.341tqq16dvg t .8)olav. ju s5xupg1jr0$ \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 ando7 r(f7/eagzl they spot each other when they are initially 11.0 km apart. How7gr( foe/7 zla much time do the pilots have to take evasive action?    s

  An airplane is heading due south at a wus4ebegla51zpzx:n 0*t0 g 1speed 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 Probf1tfi3z. x6zb z00k oblem 41 so that it will fly due soutzbbio 6z t0.z013ffkxh?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shore in Example 3sb xfs.woc x6+37fzr)–11.   

  A passenger on a boa h25 lw+ y+m8fo1awx 8fr b9-g3ydsyfgt 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 speed v cm,42ny-qqdt.z4q yin 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 still wat3liup cj:)pbh 1eo.-.vc m 0vper is 1.70 $\mathrm{~m} / \mathrm{s} $, must cross a $260-\mathrm{m}$ -wide river and arrive at a point 110 m upstream from where it starts (Fig. below). To do so, the pilot must head the boat at a 45$^{\circ}$ upstream angle.


What is the speed of the river's current?   

  A swimmer is capable of swimming qx(g 8b+sl; mvy5x(0kff ;xs j0.45 $\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 190gwq)7z slmrnd0zb $\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 6*h0m p4 onid6 1+q/24okzij.x0whj fzz2pzh g20$ \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, travelin8 8;lcq;* b*ffbxpkeq.f i 1cfg 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’ :yf 3mfrh4wx9.wa m-hs speed is not known. If the police car accelerates uniformly as given above, and overtakes the sp:rmx 9w3. -4affymwh heeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a stre vjq*7(by;: *6-p st w ca7iyo0b+cobnz8oydmet corner at right angles to each other (Fig. below). Car 1 travels at a speed ;ytyozob7 *(y v nd: 7sm*op jbwq-b0+68i cacrelative 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 of 27k62cp t+q/d by*c)jlj m . When William aims directly at the apple, the arrow is horizontal. At what angle must 2b6l pc) j yt/dqjkc*+he aim it to hit the apple if the arrow travels at a speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25 m south, and the de3 mv .-qztz7z.xjv.:n r;skn 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, y is north, and z is up. tk3; -dzjrznsev : zxqv...m7

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, esc4f1h r. rpb a3j/kcut7ape routes are sometimes placed to the side of the road for trucks whose brakes might fail. t1br73.fkjac4 p/h urAssuming 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 pz)g gxiac97+ clane) whose magnitude is 88.5 and whose x componen)z+c 9 cixg7gat 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 angl-.h;2o l cucpke $\theta=30^{\circ}$ 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 wmy3h9 ndq0jn :dj g:-tuf,*wnuf24 + vrg,ccdue 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 tvw-a 36l-ry 2 7c7twik6poej$\mathrm{~km} / \mathrm{h}$ 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 jumperoao+kr a802,v (cnpdx is capable of jumping 8.0 m . Assuming his horizontal speed iskvarc(d 8oxan 2,0o+p 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 toowv s+mtt*z;.r k 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 in both cases.vrt; *+mwstz, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over the e9ole7e- gyh .b *gnwcio2/r3 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 horizax 0pd35wve,1mrj r,11xdc e5 ign(jg ontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water level that 5prw11,iad3je xg5nvjr1,(dm c0xg eextend 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 is necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontally. What minimr4; xlr:t 5onzum speed is required fn45:;rxlzot ror 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 adz,uvyq4uui084 spj ) 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 wau6 orkt5,m4uyk m4 bz:xe i1ti2pz2 i0ter is v . The boat is to make a round trip in a river whose current travels at speed u . Derive a formula for the time needed to make a round trip of total distance D 2ymio:1p5xm 0ktiet 4 z 6 ubz2,uikr4 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 launu2qy b2(zaf,4rup: 1td65ky1qe,)d p jtcah dched from ground level to the top of a cliff which is 195 m awat2rud,c5yapq yjde (4k1z) p2fqbdu6,a1 th:y 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 heigh c:6qfv n0w c8a2sh/qet of 2.10 m above the floor. The basket is 2.60 m above the floor. Theqeaf8 nvq0c/h: sw 26c player likes to shoot the ball at a 38.0$^{\circ}$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22 \mathrm{~m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves the end ofogv;s8 w/1,eiy2xx xu 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/iwrxzmzn,o+o og: - 1 to make his car jump over eight cars parked side by side bel+ wnm-xo :rzg1,ioo/zow a 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 why) 9+e(brox a+yvc :kyich leaves the bat 0.90 m above the ground at an angle 9vo yyr y+(c):+xea bkof $61^{\circ}$ 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 wee0c-lmp di4pir- kq ;i/t42vith 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)f2c)abr:sbt ayw (f je(: us2 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 g)g yhc ec.mu q3vk87ot((x7lyou decide to do a quick calculation to finduggyhc ltc )(xqe3(7kv.7 m o8 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 your gun?