One car travels due east at and a second car 4v rwor.cx)8ztravels north at Are their velocities equal? Expl)z.vrwc 4xor8 ain.

Can you give several examples of:67 tq) hze,pwtnm x bl/(0tze an object’s motion in which a great distance is traveled but the displacemenq (,z 6m:htlttbewx/0e)nz7p t is zero?

Can the displacement vector for a particle mom k8qee uhk k w2w.svy.x8421sving in two dimensions ever be longer than the length of path traveled by the parti88s kvhsue22q 4.1. w mkkweyxcle 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 lengx h:b47t;*oimeygl; : :3qydd;xkp d jth $ 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 u( bgydsi-f,dy+- 5.pf rx)3d iqjeg8vnequal magnitude add up to give the zero vector? Can three un qfdbs -p dxyj+ )g8i.(3erifyd-g5v,equal vectors? Under what conditions?

Can the magnitude of a vector ever (a) be equal to osunuw0z iae0m.-+) 8o5 rxkwt ne of its components, or (b) be less0wmz) + nstk8rou50x.ea -uwi 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 a6k4l: kpc5 z ye:hw6ut moving “car” the riders first hop onto a moving k 6ptlcew5:kzy 4u 6h:walkway and then onto the cars themselves. Why is this done?

If you are riding on a train that speeds past another train movc-wi, svyub672pdn *h ing in the same direction on an adjacent ncu7bid,psv 2 *-y6wh track, it appears that the other train is moving backward. Why?

If you stand motionlsmei( 3fj/hy.mz -e*q ess 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 if they remaiq3 h.eejymmsiz f-* /(n under the umbrella. Why?

  A person sitting in an enclosed train car, moving xxylh90dy9n 1 at constant velocity, throws a ball straight up into th0hln91xx9 y yde 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 can5zc5 (*0fq;dqv z.qvz8ckgwc row at 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 the starting point. Which8wq gqf (* q;0.cczk5vzzv5cd rower reaches the opposite side first? ----待选择----AB 

How do you think a baseball player “judges” the f,3qyu3eay1xu k:cv9*j 0ou jl qs; yi,light of a fly ball? Which equation in this Chapter becomes part of the pj3uq ju 39uy;l ycaq:,yxv* ise1ko0,layer’s intuition?

In archery, should the arrow be aimed7.f qs7d1; j.:hmkda ohkk ow9 directly at the target? How should your angle ofw k1ao.:9. mqkfdhkd7ohsj ;7 aim depend on the distance to the target?

  A projectile is launched at an angle of i:v.p.pr3oy 2v-94iw li 9x kxogdogu8vm84 c$30^{\circ}$ 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 idejr1 cw;f 1.xcrntical initial speeds, but with1 .j;cc xfw1rr $ \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 k)to(4eswx( f;zjv+ lx m west and then 85 km southwest. What is the displacement of the car from the point of ori+ljx(evst zx ow)(;f4 gin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north,i(:an)h+wgtjv an 92.d59twop wwc x2 10 blocks east, and 16 blocks south. What is its final displacement from the origin? Assume the blocks are equal leng59.oww+hwgwjnd2av) c 9:(2ip t txn ath.    blocks

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

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

Graphically determine the r q m:be.5qe1 yl2fhg*besultant of the following three vector displacements: .bf1mlge2ye qq*h:b5 (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 veqs np.:kga; 8;rdf*xictor $\overrightarrow{\mathbf{V}}$ 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 traveutwxeu ;kq)a1( **ewwtdkl sm wz,1zw/1- i p9ling $735 \mathrm{~km} / \mathrm{h}$ in a direction $ 41.5^{\circ} $ west of north (Fig. 3-31). (a) Find the components of the velocity vector in the northerly and westerly directions. (b) How far north and how far west has the plane traveled after 3.00 h ?(a ) $ v_{\text {north }} $=   $v_{\text {west }} $=    (b) $\Delta d_{\text {north}} $=    $\Delta d_{\text {west}}$ =   

  Three vectors are shown in Fig. below. Their magnitudes are gicg zz by/73lb1;gno5even in arbitrary units. Determine thebzg b3cz7 go5ye;/nl1 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 vectorsj/ bul a/l0ee+ $ \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 map to 3 d93caevyay6; r;bdk be 4580 m horizontally fro;3;y 3 vadbaydek6 r9cm 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 magnitudl;kh82yri1y-x+9re e i4d zg je of 70.0 units and a y component of What are the two possibilrjlkye-14rxydz289eh + i ig ;ities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock) : 3toimsnup;ni8y. o with a speed of How far from the base of the rock will sh ;ps i:inomto.n)y83ue land?    m

  A diver running dives out horizontally from the edge of a vckdmajb-pk 0.3hcu/5 ertical cliff and 3.0 s later reaches the water below. How high was the cliff,kcapb0mh-k /3. jcd5u and how far from its base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near th3 aaa 6d5ef:yce ground shoots water at a speed of At what angle(s) should the nozzle point in orde 3a:ya ef6d5acr that the water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebb b si(x ge4dsn.ut1*jb1 509xug6jyjlles 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 pebble6 gs*n j5g.yt(1su x4dj0eb9x1ui jbls going when they hit her window?    m/s

  A ball is thrown horizontally from the /. qcwnhsn;)a x9-t)(qlcfw qroof of a building 45.0 m tall and lands 24.0 m from the base. What was the ball’s initia -)wl sc9wx.f) nn cqqa/qt;(hl speed?   

  A football is kicked at ground level 0y2uar:4:i gazj 8a wpwith 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 horizontalync+f-hyk, ggr0; v1fly at from the roof of a building lands 36.0 m from the vfr 0 hgfnk-yc+1 ;gy,base of the building. How tall is the building?    m

  An athlete executing a lol c6o1+*tna0 rjj ewr1ng 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 jump on the Moon as compared tol/5 .mq0r)wnsfmekh , the Earth if the takeoff speed and angle are the same. Theewskmlmf 0h q).5 ,/nr 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 sam-krvxeax/w:o ikp3 qv 48y47r e 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 t1n;a efln-gz ,raveling wants 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 ove-;nz,l1 nfga erhead?    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 firedm4fzx11ojs *d with an initial speed of at an angle of 34.5$^{\circ}$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot from the edge of axs7 bc(m9m)g pcfy.4;i lya+u cliff 125 m above ground level with an initial speed of at an angle of 37.0º with the horizontal, as shown ix;miy m4gf(.cu cys7 9lap b+)n Fig. below.
(a) Determine the time taken by the projectile to hit point P at ground level.   
(b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find   
(c) the horizontal and the vertical components of its velocity,   
(d) the magnitude of the velocity, and   
(e) the angle made by the velocity vector with the horizontal.    $^{\circ}$ below the horizon
(f) Find the maximum height above the cliff top reached by the projectile.   

  A shotputter throws the shot with an i.: +4psrra;pf6lmg 2s 38f ijtnz.dfjnitial 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 /go iyr8x3-tn projectile equal its maximum height?int/yr8og3 -x    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with tv2xyo1 i t)y:rwwnm0p 7l5zy7he slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that agaip5yi7ytxnzv107 )m2 w:wyolr n 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 mountain climberskc ja (8rg.bt3m/ gm7fvgt /;x on a rocky ridge 235 m below. If the plane is traveling.k ;8t /3cm vja x/7gf(gbmrgt horizontally with a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

(a) how far in advance of the recipients (horizontal distance) must the goods be dropped (Fig. a)?    m
(b) Suppose, instead, that the plane releases the supplies a horizontal distance of 425 m in advance of the mountain climbers. What vertical velocity (up or down)  ----待选择----updown  should the supplies be given so that they arrive precisely at the climbers' position (Fig. b)?    m/s (fill in magnitude here)
(c) With what speed do the supplies land in the latter case?    m/s

  A person going for a mornbpkrpg8z *f: 6oqr (y f1fq8v7ing jog on the deck of a cruise ship is running toward the bow (front) of the ship opf b6qr gk:f1fzyp8 (r*8v7 qat 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 s8df)axrx/gprx/ rn:cx8b:xck 5q(1 wpeed of 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 highway at 2ge wop la:t- n:sa(9+i5 $\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 2.37,kvf ov;i, vg0$ \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 spot2n*0-wlhzfsc n 0t9) k9nrbi r eachzt9hrnw flr *-9)bksni0 2c0n other when they are initially 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is headi0ft:: g fvp0z3 ,zs. ncl;townng due 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 infgd c nb7f)easf-;) ew p ywfv21i1l5+ Problem 41 so that it will fly due ai vfbsfc-fd)gp;2wyf5n11lw e+ 7)esouth?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shore in Ex l3sv5d;8 mzueample 3–11.   

  A passenger on a boat moving at ytc9nb:p7ar(hv o. wum1:j u+ 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 ign)3zmkahs .m:a90f cs 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 waterky+8a* e-usp uwtlh iisn(;58 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 ofu0:34ys ecck iaj*s+t swimming 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?   
(b) How long will it take her to reach the other side?   

  A swimmer is capable ofqn vp s207(nx;o/6si t rko-hb swimming 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?    $^{\circ} $
(b) How long will it take her to reach the other side?   

  An airplane whose air speed i vo+t/qy*n(h* v3umuas 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, travels:roo4g46t w:ssbu n2c2 k 3tqing a constant 95$ \mathrm{~km} / \mathrm{h}$ , is passed by a speeder traveling 145$ \mathrm{~km} / \mathrm{h}$ .

Precisely 1.00 s after the speeder passes, the policeman steps on the accelerator. If the police car's acceleration is 2.00 $\mathrm{~m} / \mathrm{s}^{2}$, how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)?   

  Assume in Problem 50 that the speeder’s speed is not kq,nq46, qppvt2.j finnown. If the police car accelerates uniformly as given above, and overtakes the speen tqp2pjf qq6.4vi,n,der after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner at right angles to each other (F*4 vqmsgxgc x;/64lxzig. below). Car 1 trzcg4lv64q/ m xs*;xxgavels at a speed relative to Earth $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , and car 2 at $v_{2 \mathrm{E}}=55 \mathrm{~km} / \mathrm{h}$ . What is the relative velocity of car 1 as seen by car 2 ?    km/h    $\theta$$^{\circ} $ West of North
What is the velocity of car 2 relative to car 1 ?    km/h    $\theta$ $^{\circ} $ south of east

  William Tell must split the apple atop his son's head from a e rix ux.;b,,ldistance of 27 m . When William aims directly at the apple, the arrow i.r,l;xeu, bx is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25xv-yzqfcz8oo i.lx; yq69: a, m south, and then takes an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, ax6yzq;8 lzv,o f-yxao 9q.c i:nd 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 ieyl * :,hq )s08jogtc 9ahh6rthe side of the road for trucks whose brat:9eq a*olj gci0, hhh 8y)r6skes 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 compon:tev-i,:u ph qs k.:gg( (opunent of a vector (in the x y plane) whose magnitude is 88.5 and whose x q-.utsgvg:eu (: (:ppkni ho, component is
75.4? What is the direction of this vector (angle it makes with the x axis)?
$\text { Direction }$=    $^{\circ}$$ \text { relative to } x \text { axis }$

  Raindrops make an angle t+w(y0 oad 3q4ss1 dpe $\theta=30^{\circ}$ 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 speed of 1 jft:jcm 4tt47h/z)rz3:phfr55$ \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 p.-wu4r 8 ektyad;a-yq l-,mr $\mathrm{~km} / \mathrm{h}$ 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 . Assuminhvbal++ 3*tl eg his horizontal speed is3+ah ll*vt eb+ 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 “ q9y6,obm /(r.tldwernine iron” to the Moon and hit a golf ball about 180 m! Assuming that the swing, la(dr l9m.tq y we/bo,6runch 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, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer ot g*j9(d -/cd)u1fwrf:yrui: nb+rrover 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 pus)kv ok)( 8zypmz)c(6uyvgn ;oh off horizontally from rock platforms about 35 m above the water, but 6zy)))vmpv zy (gkn(ck o ;uo8they 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 is necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontally. z uj)uwd36x c ezckg,;7omg-92/i ird What minimum speed is required for the ball to cc63; 9uzkxw e7)j ig 2-dz,iduroc/mglear 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 con 1bodxxtg-* w3stant $215 \mathrm{~km} / \mathrm{h}$ 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 nh:,8;lp xyhgj f2d z1 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 if the boat x ghz1n 8plhj,y ;df2: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 r 21kcqf .- ayx0rlpfe -lz:x4ground level to the top of a cliff which is 195 m away ae r1x: 4xl0-rcfplaq -y.kfz2nd 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 a3++leu c e29vcbu0x fxt, 3npp player's hands at a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The player likes to s 3nppucx02 fbeext,uc9v l+3+hoot 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 . vq el )oyg/s+qh-wj.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 hi3mqkf8(ig kt0s car jump over eight cars parked side by side below a it(3m0 kk8g fqhorizontal 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 the72fdt .s.soe s;qn(b*k m 78ezbwxmemf/1u2 y ground at an angle of smkywxfob *qes/zmt27 e28fm; s 7. (.bu ned1$61^{\circ}$ 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 n1wkya ei*n 5 vz9:t.cwith 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 bu ; c6 wizwu:sns*75j6jax c.puilding 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 guj/b.pkw.mx3v 3vf fs 4v nj/*mn, and being a clever physics student you decide to do fj m/np3 j/fvs*.4mwxkv 3v.ba 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 your gun?