One car travels due ekd0bkzpgq14m2x7 b s3ast at and a second car travels north at Are their veloc4d kbmqs32bzx7 k p1g0ities equal? Explain.

Can you give several etrw d:ev1cj b63o6:ssu /)vqexamples of an object’s motion in which a great distance is traveled e)b cq /6rw: sdv3ejs:tov61 ubut the displacement is zero?

Can the displacement vector for a particle moving in two dqsob(*1z(q /z . lszvmimensions ever be longer than the length of path traveled by the particle over the same time intervalz1/zbvq* .(qz( ssom l? 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 lenghtz).b) vk,yg-q 0bok th $ 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 3: w;reekkz me)g+9 vyup to give the zero vector? Can three unequal vectors? Under what conm9;z+ v ewk rke3:e)ygditions?

Can the magnitude of a vector ever (a) be equal to one of its1hz+v/j5mz+vp/ kd uc components, or (b) be less than one of j+chzk5z/puv1v m+d / 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, cs8+ a dm4*u;fk q*pqvto get on a moving “car” the riders first hop onto a movi4q smu+;*fk*q8dvca png walkway and then onto the cars themselves. Why is this done?

If you are riding on a t ezrx79 v7qdk)rain that speeds past another train moving in the same direction on an adjacent track, it appee )77x zdr9qkvars that the other train is moving backward. Why?

If you stand motionless under an umbrella in (vxv ratd uld)e.d1y(,-; pe3p1d)tpe) wzona rainstorm where the drops fall vertically, you remain relati) 1zeo)tlewd3r. d p(d-vnu pyt x)ap(dve1;,vely dry. However, if you start running, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at constant velocityr5f06e voa0b a, throws a ball straight up into the air in her referencrf 6005eaa bove 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 stilheputm9 u8d-)l 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 oppos 8hdup)e u-tm9ite the starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baseball player “judgiw qtc(e5+w *ies” the flight of a fly ball? Which equation in this Chapter becomes part of the player’s intuit+wq(i5t i* cweion?

In archery, should the arrow be aimed directly at the 2)q3vj yzxfj3q *g 7ax sv0a)wtarget? How should your angle of aim dependwz*g))3 a fsyjqx3q2xavv j0 7 on the distance to the target?

  A projectile is launched at an angleb/7 ti gbw5m j3(o,j83ubt3,h b gik2-ifenln of $30^{\circ}$ to the horizontal with a speed of $ 30 \mathrm{~m} / \mathrm{s}$. How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch?   

  Two cannonballs, A and B , are fired from the ground p)4rv gwn: m.ff2rvh/) ,v-tcbpiq p 6with identical initial speed:rrvt gvvi4)n/6p mbpqhc 2,. f-wf)p s, but with $ \theta_{\mathrm{A}} $ larger than $ \theta_{\mathrm{B}} $
(a)Which cannonball reaches a higher elevation? ----待选择----AB 
(b) Which stays longer in the air?  ----待选择----AB 
(c) Which travels farther? If the angle of a is 40 $^{\circ}$ the angle of b is 30$^{\circ}$  ----待选择----AB 

A car is driven 215 km w h/,rrszsvn u d0)x aay.k-,-test and then 85 km southwest. What is the displacement of the car from the-as) krz/uy xd0hvn-st,, ar. point of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 bloz9j wzhn191xib51ta jcks south. What is its final displacement from the origin? Assume the blocks are equal 1txjznzjh 9wb 159a1i 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 disp ,ym eov8jg.5vnn/zj6lacements: (1 znjv.ym n8g6jev,5 /o) $ 34 \mathrm{~m}, 25^{\circ} $ north of east; (2) $48 \mathrm{~m}, 33^{\circ}$ east of north; and (3) $22 \mathrm{~m}, 56^{\circ} $ west of south.

  The components of a vector t21yr 7p4u pvb2m g blt+9p9bi$\overrightarrow{\mathbf{V}}$ 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 9wzl0w m,6lne $735 \mathrm{~km} / \mathrm{h}$ 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. Thedz+e)ow r zzxsc59jdw( 5w -*xir magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the r zd5jxwx(+z)- ws doz 9*recw5esultant in terms of (a) components, (b) magnitude and angle with the x axis.


$(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}})_{x}$ =   
$(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}})_{y}$ =   
$|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$

  $\text { Determine the vector } \overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{C}} \text {, given the vectors } \overrightarrow{\mathbf{A}} \text { and } \overrightarrow{\mathbf{C}} \text { in Fig. below}$



$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$

  (a) Given the vectors nqtlq+ f96x(o+bbev , $ \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 basec-nff*ji5y9c camp, is measured on a map to be 4580 m hornc*yc9j f f-i5izontally 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 vectomdki /,gnc.ss4m,zj9 e*p2n,4ufphzr in the xy plane that has a magnitude of 70.0 units and a y component of What are the two possibilities for its x component?,i z p, m9gs h*/ku.j4n4fcemn,p s2dz x = $\pm$   

  A tiger leaps horizontally from a zi z/z3)ps9l.pi uy toe kg;,26.5-m-high rock with a speed of How far from the base of the rock will she ll;o32/p9ekspz. ,u tziz) iygand?    m

  A diver running div56xq(mzc64tgf*wfqq lz vp2 p:3w es -es out horizontally from the edge of a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its base did the div2 w 6(txf*ws3-5cg4fq lpvzpeqzm: q6er hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water at asup+r: g* v6ux8yha*a speed of At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why *pgaxur+sy ha8* uv6: are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s v-lhg;ym om08window, 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 ;v8gmolm h0y- base of the wall (Fig. below). How fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontally from the roof of a building 45 urj5*)zi w-fd.0 m tall and lands 24.0 m from t *)wzfiu 5jdr-he base. What was the ball’s initial speed?   

  A football is kicked at ground level with mqkquh7-8 c :na 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 j-xsq4, wthymv 28z u;building lands 36.0 m from the base of the building. How tal8hm- y2,svjtx 4 wzqu;l is the building?    m

  An athlete executing a lo 7vul7 8t nplakp5s 4tr,5n,yjng 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 bvjw8nsm,--shnv3 emy15/8eiq p 0 l ft(axn;person can jump on the Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration dsb 0nnmj ie-1y vslxe8t (n-3v,f w8qph /m;5aue to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level)iv3eh)*jn b,xoz: 4cikfa0 l. 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 flood vicykvn 2omr2wnsmbhsx:/6 jn +n 3 ,e5g,tims isolated on a patch of land 160 m below/ng,bs2n e wknh+jmr xy,o23sv6mn5:. 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 an angle of 34*r 4zr cmz h3s.zj(,ts.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 rx0t zs8*z3pkoyo.5cm above ground level with an initial speezy5oco z*tx0 r.3psk 8d 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 with an jeoi0h2.hh i4initial 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 projectile equal its n lu;nq ;. i/uulwh7+cmaximum heightl;;n7+ iu/c.u uhwq ln?    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy wiv :7ummi*i)-c +u-w sly:t jqq o9lbb+th the slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by letting go at the momi -bvuc:79 y*o+t) uwjmq+l s-milqb:ent the water balloon is shot.

  A rescue plane wants to drop supphf1rvl bchb-a5bgu1,-v .l,j lies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling hori- v,h bcbg.aj5 ful bl1v,r-1hzontally with a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

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

  A person going for a morning jog on ty(ec l:jx7.t 0m5,gstw 5yd sjhe deck of a cruise ship is running toward the bow (front) of the y5de:tlwy .j xcjsgm s0t 57(,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 sf2bce bp4*is,8 edi.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 c4)sr3i*s7 sj fea oc3at 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 2.3; j)5onh3prd/ mzcq5v 0$ \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 v1xfy bjuz4kab+-1p0n- ujl,,4sd b h and they spot each other0 411 ,l4+nj-vu,b hx d- faspzybjbku when they are initially 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is heading due south atx g-pww(n)8 ;qxrv;g y 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 pkmv *5a 4rnxku*y4:vhe i p00the pilot aim the plane in Problem 41 so that it will fly :ynk x04m*au 0phv5*ievr4k p due south?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shorecozm 7e;sz o g-fh/k:ry xw/73 in Example 3–11.   

  A passenger on a boa4 s. u1,lvlneft 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 in still water is 2hmm q jk.8 (s32c tz,kmka1exbkl 52l1.60 $\mathrm{~m} / \mathrm{s}$ 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 watf; ddh6-lt8kugxfcs r xu6*)8er 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 sn/bn,)b*j.d qm*bd1hbs :vqu wimming 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 b -f 6tt6twp5t 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 speedi40hyo;vkgfuf mxe:50)8vg d 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, traveltsua)sm:y3gd lp .0t7 nq eo,gl(:t q(ing 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. If*wr btrfqi(7 r33 )vxjgei-gkp ouko:0c; a,4 the police car accelerates uniformly as given above, and overtakes the k37 kxv r-r 3ago r qowepg0b)c:*t4(jii,u;fspeeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner at right angles to each othe rhpf, oo8*e9*czm 4gzr (Fig. below). Car 1 travels at a speed relative to Ear fo z*m94e *crghp,oz8th $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , 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 iyb0kh-cm-6n t.e ,5;yxg hwja distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aim ;ceyb-- y.hwg6 thk0mn ,xij5it 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 1 p:e8xsf g1tdq,mk7d 8xo*z uand 25 m south, and then takes an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to hut*:8 ,81pk7m fq1egdzxs do xis truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

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

  On mountainous downhill roads, escape routes are 8wt0,ubx-lmp jz.s ;lsometimes placed to the side of the road for trucks bzull ;ts, 0-.wx8mjpwhose brakes might fail. Assuming a constant upward slope of 32$^{\circ}$ , calculate the horizontal and vertical components of the acceleration of a truck that slowed from 120 $\mathrm{~km} / \mathrm{h}$ to rest in 6.0 s . See Fig. below

$\text { The horizontal acceleration is } a_{\text {hoiz }}$ =    $\mathrm{m} / \mathrm{s}^{2}$
$\text { The vertical acceleration is } a_{\text {vert }}$ =    $\mathrm{m} / \mathrm{s}^{2}$

  What is the y component of a vector (in the xud4( 8(e caol857vt js +oneyhdh/ko4 y plane) whose magnitude is 88.47dlv hdan (h8+e/k4o uo cjs(tey5o85 and whose x 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 angl+;ms6gnp jwvq: 8dc0jiv v viw95*dc5e $\theta=30^{\circ}$ 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 speedjt,n0nm-g( mlmo 96d s3sdt .z 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 60zuts.47e ezypw s1o 4i2h be$\mathrm{~km} / \mathrm{h}$ 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 ,luh:tf2ie vd.1njn:k7)q gvcapable of jumping 8.0 m . Assuming his horizontal speed is kn h1,vln :2jgv. efqtiu7:)d9.1 $\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”jx. yh;e 2qzw: 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 acceleratioeq.hyj;x zw: 2n 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 hoe- n7 eoqcsocs3 56)hp) ut,p goudpb;udk+6 0mer over the 7.5$-\mathrm{m}$ -high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat?    Assume the ball was hit 1.0 m above the ground and its path initially made a 38$^{\circ}$ angle with the ground.

  The cliff divers of Acapulco push off horizontally from rock plamdopa0 fcf38dyu95j ie k lk ..as+*w1tforms about 35 m above the water, but they must clear rocky outcrops at water level that k.ea suo d5.8j*3mcw1f9+y0ak fli pdextend 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 aitn8yg); f mm yzb+emh75xiec0n4w5; ) o;lisems to hit the ball horizontally. What minimum speed is required for the ball to clear the 0.90-m-hi );7i0x bmmcshye4ft;g) m8 zi;5ewe y5n+o lngh 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 g- y- 8aie(v.ujip0 sdconstant $215 \mathrm{~km} / \mathrm{h}$ horizontally in a low-flying helicopter, wants to drop secret documents into his contact's open car which is traveling 155$ \mathrm{~km} / \mathrm{h}$ on a level highway 78.0 m below. At what angle (to the horizontal) should the car be in his sights when the packet is released (Fig. below) ?



$\theta=\approx $   $^{\circ}$

The speed of a boat in still water is v . The boat is to make a round tr0o,+ o 1vypbkqip in a river whose current travels at speed u . Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving (a) upstream a,oyoq 10vp +kbnd back downstream, (b) directly across the river and back. We must assume u

  A projectile is launchw/ kf k ;,tf57rtkus6hed from ground level to the top of a cliff which is 195 m away and 155 m;,k k 5rthswfu7k6 tf/ 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 plaoa) h4hxsx55n :fz)t os 62szzyer'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 shoot the ball az6 ztxs zx)n)fso:25 h5s h4aot 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 ew, bn0n 3h;4rbnb l7*w afy2xnnd of a $5.0-\mathrm{m}$ -high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine
( a ) her initial velocity, $ \overrightarrow{\mathbf{v}}_{0}$ ,    ${ }^{\circ} \text { above the horizontal }$
(b) the maximum height reached,   
(c) the velocity $ \overrightarrow{\mathbf{v}}_{\mathrm{f}}$ with which she enters the water.    $^{\circ} $ $\text { (below the horizontal) }$

  A stunt driver wants to make his car j y.mtresk r . u8j-x*ix(:exs,ump over eight cars parked side by side below a h:*rx8 xm -t ke,i(jx. .syeursorizontal 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 lea+lu neit 1qr:h0g 5 gz9p+jp-lves the bat 0.90 m above the ground at an angle of 0l+gjrnp5eql+zp g:h t i-9u1$61^{\circ}$ 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 hitswd,qi0m g 9yz6 a baseball with an initial speed of $32 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    $^{\circ}$

  A ball is shot from the top of a buildi-q*z ftfp,r+ f1 x8dzfw3jy2kng 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 sszm nz9o,q1 )mb:)fb xtudent you decide to do a quick calculation to find its maximum horizontal range. You shoot the s):of z9nb 1zq) m,mbxgun 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?