One car travels due east at and a second car travels nohn(bh+ez hkvl:sx 5+9rth at Are their velocities hln+kev5 hh( :sz+9xb equal? Explain.

Can you give several examples /h- aayrio,:p of an object’s motion in which a great distance is traveleah,a/:i orp -yd but the displacement is zero?

Can the displacement vector for a particle moving in two dimensl5r1.f*gdg 0htvz ct g9(1cxeions ever be longer than the length of path traveled by the particle over the samegtgvz .l1x0r9hd(cftc g 51e* 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 lengthgr1jdws 1 )j3m $ 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 adhgor f d0.9+isb.vfz: d up to give the zero vector? Can three unequal0dis.+zf .9 h fb:govr vectors? Under what conditions?

Can the magnitude of a vector ever (a) be equal to one of its com6b)ksd7 d.a qi*mw9iiponents, or (b) be less than one of its componedk*das96 iw)iib7 qm. nts?

  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, x 9 /v mq1jk9bn 8wohoh9h-lz.) uskd0to get on a moving “car” the riders first hop onto a moving walkway and then onto the cars themselves. Why is -zs dnv)h8b 1kkh.90mqxjhuwo/ 9 o l9this done?

If you are riding on a train that speeds past q9 hl1hy4w7unc m- s n59-u+ rvixvle6another train moving in the same direction on a vysx1c nlr m4hqu5-9eu-6hi9l nv+7wn adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under an umbrella in a rainstormju39 s o5n;yrm where the drops fall vertically, you remain relatively dry. However, if you start runniyun 59s;ojrm 3ng, 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 constants-u )xm5qg3hr 2jit.g velocity, throws a ball straight up into the air itijg s g5r2hxm )u3-.qn 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 speed in still water, set off acro fbfs ;jk9(/mg(bg f1hss 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 b s;f9h b/mg(kj fgf(1the starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baseball plalz 5m ft9pqg4 ru++zx,yer “judges” the flight of a fly ball? Which equation in this Chapter becomes part of the playe gm qp 95,4fru++zzxtlr’s intuition?

In archery, should the arrow b)c 7 46jjrz3af3ca bd-0fxekbe aimed directly at the target? How should your angle of aim depenfa3)-b7ce4j3kcr x f6azjd 0bd on the distance to the target?

  A projectile is launched at an angle ox)yfq9,st3 : zh9p w87ffg topf $30^{\circ}$ 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 identical i-u6 h)jzz6 9c c/pirghnitial speeds, buh )z 6-uzjh/rcg6c 9ipt 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 t1bi(ph* r.uryy *x/ rdhen 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagra.1hx*r u prry *(ybdi/m.

  A delivery truck travels 18 blocks north, 10 blocks(0it/ kl :mtk;vvwvg0 east, and 16 blocks south. What is its final displacement from the owt0:; ikl /k0mvtg v(vrigin? 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 following three vector displacemen;iouvww acn6(+io(+qts: (n(uiqw+;w v6oi+( cao1) $ 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 vect 8p6sm ),d6iv3f4n yae*rxwtsor $\overrightarrow{\mathbf{V}}$ 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 traveling4 xpzdgcg (u-h.i)k7d $735 \mathrm{~km} / \mathrm{h}$ 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 giv 4y/hb knp 2iz(ym(b y:opmh+7en in arbitrary un/ m+:npyiy(h4 o7mkzy (b2 bhpits. Determine 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 vectorl.0bihu/+ kw 5sg orihk p;6/h i0d,yns $ \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 v:k8-zvf qq,yv 4,z1:hk kly qexp.pt( u(cw+on a map to be 4580 m 48vhv,wy+kyq(kv: p( :1k-ux .fztzl,q q ecphorizontally 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 i g bc;:l9 tlpajz1/9nan the xy plane that has a magnitude of 70.0 units and a y component of What are theall; /cza9bp jn9t1 :g two possibilities for its x component? x = $\pm$   

  A tiger leaps horizont(4qs2yeo-hqh p pcx+gsg)qv sp8w7 + 3ally from a 6.5-m-high rock with a speed of How far from the base of the rock w qwq4)pv8sx3g pe cg py+ s7h-sq2o(+hill she land?    m

  A diver running dives out horizontally from the z *g/ zmvam4hag,8 db9edge of a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its base diaza9g/ zb *hmg 4,mdv8d 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 2 *b/rzegtso rmin ):0At what angle(s) should the nozzle point in order tha )g:/rosm2i0 zr n*tbet the water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window,( al *gv)ef-er+(g knp 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 basef +vnr(*lkge-p )ae(g of the wall (Fig. below). How fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontaln 6lqj4dod 2a*ly from the roof of a building 45.0 m tall and lands 24.0 m frajddlo*26 4qnom the base. What was the ball’s initial speed?   

  A football is kicked at ground level with a speed of 8o all1sjvn- 518.0 $\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 bujlit +i nx;:8milding lands 36.0 m from the base of 8nl;xiji t:+mthe building. How tall is the building?    m

  An athlete executing a long jump leavesr*v7/ymlqx2qbo*q/ pvy *ez: t ur)s3 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 dcu/ig63 qb:0 -fbas17ytab x on the Moon as compared to the Earth if the takeoff speed cf06db31ya ai7bx/ -qt:g ubs and angle are the same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a targeffw.g0t9 (h)mri- jd pt (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 travelin gq-g.u1j 6p lbehz54ng wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies shouldg lzj5g4hep qu1. nb6- 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 an a b6md qeveh-l+xe--z pt q5;4hngle 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 ob3wdck1 e c-:wk)yhq 5f a cliff 125 m above ground level with an initial speed of at an angle of 37.0º with th) 5hwec1ycwq: - 3kbdke horizontal, as shown in Fig. below.
(a) Determine the time taken by the projectile to hit point P at ground level.   
(b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find   
(c) the horizontal and the vertical components of its velocity,   
(d) the magnitude of the velocity, and   
(e) the angle made by the velocity vector with the horizontal.    $^{\circ}$ below the horizon
(f) Find the maximum height above the cliff top reached by the projectile.   

  A shotputter throws the shot with an initial speed of ;8ib7ft lb8etaknm 0115.5 $\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 /j 0ljlp;+mrewill the range of a projectile equal its maximum height +jl/em ;rjlp0?    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the f7-2f/ mx+2s 2rvksaqpin w;jslingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong qs2s-wixr7+ v pj2f2amfn/k;move by letting go at the moment the water balloon is shot.

  A rescue plane wants to drop suuy( 76c9 ngtlqpplies to isolated mountain climbers on a rocky ridge 235 m below. If the lc7ntu(q y 9g6plane is traveling horizontally with a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

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

  A person going for a morninfr33 0/u p zjvnhw6(tyg jog on the deck of a cruise ship is running toward the bow (front) of the ship at 2. 0hrv6z3/tu3 ywpj(f n2 $\mathrm{~m} / \mathrm{s}$ 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 0a ujqj7j,f:h3p0y.slmfn :n)s,cq: z.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 hi1713vgr a/ykh c.mqtl ghway 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 2.30n5xivnud 48 ha 70 b-pl 9w(3c8gfzbse$ \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 op b(,zfll g9u1ther head-on. Each has a speed of and they spot each other when they 9 fl1zug ,plb(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*+wm4b nxz2 ew 1*vnyna.nr 5c 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 sho:ky*ozj hp l1- ,i1ot7e ffjgzqh74x(uld the pilot aim the plane in Problem 41 so that it will fly tolkj4 yhhjzz1 :xp17 ff,g- e*(q i7odue south?    $^{\circ} $ east of south

  Determine the speed of the boat with respect 2paa85kp f4vnn qj7.y to the shore in Example 3–11.   

  A passenger on a boat moving hoiwhk/u-7 inps ,k1m;r t2e2at 1.50$ \mathrm{~m} / \mathrm{s}$ on a still lake walks up a flight of stairs at a speed of 0.50 $\mathrm{~m} / \mathrm{s}$ (Fig. below). The stairs are angled at $45^{\circ}$ pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?   

  A motorboat whose speed in still water is 2.60vm r 4ehxp (+)bjr3hxue .8g.s $\mathrm{~m} / \mathrm{s}$ 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 water is 1.hw,gfo e:/68upgla g670 $\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 :*yrx 9)m69edfm kcuk 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 0.47di5ysn ngi ;*5 $\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 spxtr4 xx6 pgp;3eed is 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, traveldp+3w+ o 1xvfeing 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 known. .09on7zrbi ec If the police car accelerates uniformlric . o9nz7e0by as given above, and overtakes the speeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner a 35ar(24jc5(eg wr nbhl- igxct right angles to each other (Fig. below). Car 1 travels at a speed relative toc(( 4cilh3 be w-2xag5j rng5r 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 t200w1v /nwl kcv6 xj*qcwsc:uhe apple atop his son's head from a distance of 27 m . When William aims directly at the apple,2wq6l00 c w/jcxk:*s cwnuv1v the arrow 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 25 m south, a85bxkcgyb vp0dw 1n6hf87 2nl nd 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 xg5 0yhp d8knb27fnl8cv6bw 1x is east, y is north, and z is up.

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

  On mountainous downhill roads, escape rouae4 cp6f3uk:tsd )uit z9pc8*m3+mwvtes are sometimes placed to the side of the road for trucks whose brakes might fail. Assuming a constant upward slodpt33ca8:i u f+t6m4k)scw v9 zm*peu pe 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 componentswl/pjim 1 dl6p,cl96 p )z2al of a vector (in the x y plane) whose magnitude is 88.5 and whose x com6l/s mlpjlc69 zi1dl a,p2p)wponent 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 ank75pp ph11qiggle $\theta=30^{\circ}$ 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 t-lht2sa4n( c 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 ;egw/c4 fz/k w$\mathrm{~km} / \mathrm{h}$ 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 (k8bmy 4tc0y lb +bgp;iuag,,capable of jumping 8.0 m . Assuming his horizontal speed is 9,ga8b( yy04b +; pbmcgk,tliu.1 $\mathrm{~m} / \mathrm{s} $ as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright - that is, the same way he left the ground. t =    y =   

  Apollo astronauts took a “nine iron” to the Moon and hit a golf glc9 9cq 7*x:4ucwbmyball 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, but on the Moon there is ngcq: cbym*ucwxl4 979 one!) g$_{moon}$  

  When Babe Ruth hit a homer over the 7.5x,+:fg5 is)zot9w 4wi nc*nd a$-\mathrm{m}$ -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 Ar2i/a(san 9pg .n8 tzycapulco push off horizontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. below. What minimum pushoff speed is necessary taty rn.a/gp(z 92i s8no clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the mc *zxkjqeh/*)4 q8fhball horizontally. What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from thej/)qfq4z**8mchhekx 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 constant fd3g*k1r+,2jv hqn-7pbz hjz$215 \mathrm{~km} / \mathrm{h}$ 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 waoln,ohmggr b 9vg.;s2)8r-,hpeh 5ys ter 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 tota-hr gpb5g;,s .e, 2vyg 9)onhor8hlm sl 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 launche5xs4az*nlzy 1 z 8do(wd from ground level to the top of a cliff which is 195 m aws1 *lz(d5yxnzao 4z 8way 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 handi y l+2/ 2(nf.;dqqtrdi mpaiu qf0g;1s at a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The player.diad; n2gif i/(r1;qq u+t0lpyf2 m q 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 of83fug 80aqlx u gl4+d9mghh+o 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 m:. j2dpywk a(/ krsto+ake his car jump over eight cars parked side by side below a horizontal js k2+(p.d: atk/ oywrramp

(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 ,1t lpb je:z6fbat 0.90 m above the ground at an angle jbp:lezt61, f of $61^{\circ}$ 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 b v7h8ce:k7kyz;s x 4xaaseball 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 t3kc*;uilp4 mi3 mut2. l fqjw3op 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 dqjk3 t7sfp ;;clever physics student you decide to 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 yourtps f d3;j7;qk gun?