One car travels due east at and a sellu xln6vo27;:av)n p cond car travels north at Are their velocities equal? l )6ol2lpvn ;u:7 vxnaExplain.

Can you give several examples of an object’s motion in whii-7l uv r62yd)ciu vx5ch a great distance is traveled but the displa iv7c)l di-u2yvr6x5ucement is zero?

Can the displacement vector for a particle moving in two digp7 k.dg* rh)mg +71i(fmozfrmensions ever be longer than the length of path traveled by the particle over the same time interval? Chim7+ .p)r gf1gzm(dgf kr *o7an it ever be less? Discuss.

$\text { If } \overrightarrow{\mathbf{V}}=\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{v}}_{2} \text {, is } V \text { necessarily greater than } V_{1} \text { and/or } V_{2} \text { ? Discuss. }$

  Two vectors have length *j5hvpee2c7/jprd;p7l jw) : vovbj.$ V_{1}=3.5 \mathrm{~km} $ and $ V_{2}=4.0 \mathrm{~km}$ . What are the maximum and minimum magnitudes of their vector sum?max =    min =   

Can two vectors of unequal magnitude add up to give the z1g .rpq1+psj/x6 s3q a(xyxc bero vector? Can three unequal vectors? Under wh1+ axj 16pg/bxs.y(q cqrpx3sat conditions?

Can the magnitude of a vector ever (a) be equal t3 kjvph7m2f 3ro one of its components, or (b) be lesshpm3k73 vjr f2 than one of its components?

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

At some amusement parks, to get on a moving “car” the riders firsm0 btc frk(;3kt hop onto a moving walkway and then onto the b3;m 0fkctrk( cars themselves. Why is this done?

If you are riding on a train that speeds past another train movin+f(k qrxt7k5d g in the same direction on an adjacent track, itrdf(tk+x7 q5 k appears that the other train is moving backward. Why?

If you stand motionless undero+fs:lui(yv1 kz5 sr: an umbrella in a rainstorm where the drops fall vertically, you remain relatively dry. However, if you start running,fo+:i vrzuy:( 1 5sslk 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 velocity, throwpv 94)rt+bes ec*1ovb 6r,af93tl tu ys a ball straight up into the air in her reference frame.atb46fc vu9 o9 yret, s*31pl)t+ebrv
(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 odd.ktv d6 vucz7tye +1,wu5j;ff 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. Which rower reaches the opposite siued+ 1 u; 7jt ,v65d.dwvycktzde first? ----待选择----AB 

How do you think a baseball player “judges” tkyi7c u n9/7s 0suhpxe9/wrc3 he flight of a fly ball? Which equation in this Chapter sn773uuy9r9//ekiwh 0 c csxpbecomes part of the player’s intuition?

In archery, should the arrow be aimed directsl-2 nv*/rxkif . d6jqly at the target? How should your anglekdjsrin- /q*62f v. xl of aim depend on the distance to the target?

  A projectile is launched at a03io)( ckidbhn angle 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 t n)qj ,d./5eju 4sqvwfhe ground with identical initial speeds, but wit.dq5,e /)n juwfqjv 4sh $ \theta_{\mathrm{A}} $ larger than $ \theta_{\mathrm{B}} $
(a)Which cannonball reaches a higher elevation? ----待选择----AB 
(b) Which stays longer in the air?  ----待选择----AB 
(c) Which travels farther? If the angle of a is 40 $^{\circ}$ the angle of b is 30$^{\circ}$  ----待选择----AB 

A car is driven 215 km west and then 85 km southwest. What is the displ t ;(hocoxs.jy0t mn;*acement of the car from the pom*t(.sxch; ojon;y t0int of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north,29-qrr.oltlhe; +gte45tmgsy c 63 qy 10 blocks east, and 16 blocks south. What is its final displat2yhee-c4 lls+qyt mr6gg .r35q9; tocement from the origin? Assume the blocks are equal length.    blocks

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

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

Graphically determine ,0 hf4lnch i gva15(glthe resultant of the following three vector displacements: (1(vg,0 inh1 agcl5lf h4) $ 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 vesz .t- )s3shueu0.xua n*lpg.ctor $\overrightarrow{\mathbf{V}}$ 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 travelin - i 9:io5nc-:qynto93iumtyh g $735 \mathrm{~km} / \mathrm{h}$ 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. bevu*pkf-+(qy w2qb1;f zc3n9p 0fphkklow. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultak qn 0- qypff;wz91hv(cp2k+pkb3* ufnt 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 vector rd,uk .af,/l+nz)w aus $ \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 mes ylk)/9l4 rmb3 e/p/gxd gqn*asured on a map to be 4580 m horiz/gs9kmqldg )p bl/* nxer3/y4ontally from the camp in a direction $32.5^{\circ}$ west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north, and z axis up. x =    y =    $|\overrightarrow{\mathbf{r}}|$ =   

  You are given a vector in the xy plane that has a mag6irs xo 0*e)e57im xtgnitude of 70.0 units and a y component of What are the two possi tex *xsiorge570mi6 )bilities for its x component? x = $\pm$   

  A tiger leaps horizontally from n2(*zvikgrvknpru0y (3 2gdj4 7b b u8a 6.5-m-high rock with a speed of How far from the ik7 gy4 0vub2ur2r kzb(vgnj3 p*n( 8dbase of the rock will she land?    m

  A diver running dives out horizontally from the edge of a vertic 29pwfldj,cx*al cliff and 3.0 s later reaches the water below. How high was the cliff, and how,p*wjl 2c 9fdx far from its base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water at a speed of At wh j.- -1 ss4emyxo3t4 sk-ai/ zo1tsyazat angle(s) should the nozzle point in order that the e4t t -osoms 1a/3i4 a-k.jyszs1yz-x water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gejq(v6 ;yvpb:n,5 nrxfntly 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 pebbles going when they hit hf6nvq;rx:(nv b5pj,yer window?    m/s

  A ball is thrown horizontally from the roof of a building 45.0 m tall anle g uti3;nk1ub v8r0-d lands 24.0 m from the base. What was the ball’s initial 3ng;kltu ir18e-0bu vspeed?   

  A football is kicked at ground level wog822z1v .cwrs( jtd hith a speed of 18.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at from the roof of a building lands 36.0 m frs );uaeeg0r cako 8;*zom the base ofoeu;*a; zagc)k0res8 the building. How tall is the building?    m

  An athlete executing a long jump leaves the ground at a ufn4 m 4apqac/b owdi9w72 d:828.0$^{\circ}$ angle and travels 7.80 m .
(a) What was the takeoff speed?   
(b) If this speed were increased by just 5.0 % , how much longer would the jump be?   

  Determine how much farther a person can jump on the Moon as compared to the Eart x gj6cg jwa,wz-f3p(3z.xwro w(u,l;h if the takeoff speed and angle are the same. Thugrx wjz, 6 f;pl gj.z(-xow3acw (3,we acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on n2y jwwv(-jk)yxz49 q the same level) 75.0 m away.
(a) If the bullet leaves the gun at a speed of by how much will it miss the target?  
(b) At what angle should the gun be aimed so as to hit the target?    $^{\circ}$

  The pilot of an airplane traveling wants to drop supplies to flood victims5y d6i sibyj8a3bx5g ( isolated on a patch of land 160 m below. The supplies should be dropped how many sesb8ygi ax5ij65 dby3(conds 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 qoot7 -v-mx7e jxgq )934.5$^{\circ}$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot from the edge of a cliff 125 m above ground level witm3lwko5 (3ro8w1db ith an initial speed of at anl5 o(wt38b idrw3mok 1 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 inindty2c l0:p :ltial 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 maximum 6gkx:bryt9,z0j9 pcw height? jcrztpg6,0k : 9w9xby   ${\circ}$

Revisit Conceptual Example 3-7, and assume that au 6uc)fb ff9r-jr/t/*-zn dtthe boy with the slingshot is below the boy in the tree (Figff )cjzd6tufur/tr b9 /a* --n. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants to drop supplies to isolated mounf(*wkcd(s2 jriig*/u 9wu6fbtain climbers on a rocky ridge 235 m below. If the pd f6gbiw*9u(/i2ur(wc kf*js lane 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 morning jog onn raqr(tlac 1v8 dw4c/i4a9 c/gh2,uu the deck of a cruise ship is running toward the bow (front g ,anr(dqhl4/ aw4u2 r v1i8cacutc/9) of the ship at 2.2 $\mathrm{~m} / \mathrm{s}$ while the ship is moving ahead at 7.5 $\mathrm{~m} / \mathrm{s}$ . What is the velocity of the jogger relative to the water?    m/s
Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?    m/s

  Huck Finn walks at a raxz14 qnkub 5ut+ :k:zt3f1nspeed 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 2,oxsljg2igf -(h /y6 g5 $\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 2.3k +sp0i;gq*o kkteo52,u+s3d r0 dy lo0$ \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 aheqncn9i 0g)ufr /5dc; .c2b3 vexru 6 speed of and they spot each other when they are in c 6r2.v3)cxn neeq/f0ug; hdciu59britially 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is heading due south at a speuzg(jil dp0h65hq:m:xxl 8ae 2/(aq ted of 600$ \mathrm{~km} / \mathrm{h} $. If a wind begins blowing from the southwest at a speed of 100 $\mathrm{~km} / \mathrm{h}$ (average), calculate:
(a) the velocity (magnitude and direction) of the plane relative to the ground, and    $^{\circ} $ east of south
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.   
[Hint: First draw a diagram.]

  In what direction should the pilot aim the plane in Problem 41 so z.:1tx76dd/- lphxc+bef b7 s l7dtrq that it will fly due - 7 dh1pt. bz+btqle /xd6xcrf:ds77lsouth?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the sx dvi6mg h;t (,q8u-hqhore in Example 3–11.   

  A passenger on a boat moving at 1.50.sm5xso 44ti w$ \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 watermuofv( u:pj,k*w-5 ry is 2.60 $\mathrm{~m} / \mathrm{s}$ must aim upstream at an angle of 28.5$^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current?   
(b) What is the resultant speed of the boat with respect to the shore?   

  A boat, whose speed in bm7:+ry-)holjr *r+nkk 0hpa still water is 1.70 $\mathrm{~m} / \mathrm{s} $, must cross a $260-\mathrm{m}$ -wide river and arrive at a point 110 m upstream from where it starts (Fig. below). To do so, the pilot must head the boat at a 45$^{\circ}$ upstream angle.


What is the speed of the river's current?   

  A swimmer is capable of swimming 0.4 8:3vfubl6ztujf1 n gy(-ip7zw,j ur35 $\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 0ssh*)s;ns (fg1hkg7w .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 speedk) n :cqfwh5i.(5q wtp 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, traveling ay(mby v 42f4jr 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. s(8b h z7 *omznlnui f8:)aixdq0n2p0 If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, whatu*n hf8nd:a z7i 8bx)o(00 s z2lmqnpi was the speeder’s speed?    km/h

  Two cars approach a street cornz2m5l0ckghg hpoq82 +er at right angles to each other (Fig. below). Car 1 travels at a speed relative to k2mqzp5 c lh2+ h8ggo0Earth $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , 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 tiy6 j z+ .je5g*1rrq ) vh. 1y.pq7naczjbwwd3he apple atop his son's head from a distance of 27 m . When William aims directly at th. cpjyrwd7 qvi n* g)zj.h1bjw qy+ 6.51z3erae apple, 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, and the mhy9mm.zx u62p :-juaml(m,nn takes an elevator 10 m d-xj hmm2,9mp mm n yla(u.6u:zown into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

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, dr.f9eix8wryv,s,5 /w11zn zbmweieb:5 ht6 escape routes are sometimes placed to the side of therszi wzr.x,/n,18wbv1 y mtbed we55i:9efh6 road for trucks whose brakes might fail. Assuming a constant upward slope of 32$^{\circ}$ , calculate the horizontal and vertical components of the acceleration of a truck that slowed from 120 $\mathrm{~km} / \mathrm{h}$ to rest in 6.0 s . See Fig. below

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

  What is the y component of a vector (in the x y plane) whose magnitude is f:g5t4g ra j3v88.54fjgg:ra 53v t 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 angh ixk+(c9xa4t le $\theta=30^{\circ}$ 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 3 j xv,4q)spqa155$ \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 z5n 9k)tjii6r4 2lodg0vhi7x $\mathrm{~km} / \mathrm{h}$ 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 jumpin n c or//c8ahfd7ec,5rjo*j2(v w9;nspn js6s g 8.0 m . Assuming his horizontal spee9epdw8consc hjo/ ( sf,52/j*rjnn;s 6 avc7rd is 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 “ninfw,0p*(,)rev) d mnwdz 9 kyvid(noq 9oz.4sve iron” to the Moon and hit a golf ball about 180 m! Assuming that the swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon(,dvn f*r,k0y z)o pv9d4 w)oe inz(ds9wmv.q. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a hj gpwyoqa +5txp9n ,7-omer 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 rockso d*tts,g n)*ss.wu)xjr4 1k platforms about 35 m above the water, but they must clear rocky outc1w)n tdrjk oxss ,sgu) *.s*4trops 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 horizontal8m6y;buer2 evi6l +lv ly. What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball 8;6mrv ee2 ly6+uvlbiis “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 tc(5tvfu(3fi;k,cne stant $215 \mathrm{~km} / \mathrm{h}$ 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 44gs o- ek)ipbtrip 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 and back downstream, (b) direc i-pksogbe4) 4tly across the river and back. We must assume u

  A projectile is launched from ground level to the top of a cliff which+)bjhfeb:oxl 8b.zk up l cerba, 0:/3 is 195 m away and 155 m high (sk r)ehfzpblj: o3,:.xa eubb0 +c/ 8lbee
Fig. 3-47). If the projectile lands on top of the cliff 7.6 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance.



$v_{0}$=    $ \mathrm{~m} / \mathrm{s}$
$\theta$=    $^{\circ}$

  

(a) A skier is accelerating down a 30.0$^{\circ}$ hill at 1.80$ \mathrm{~m} / \mathrm{s}^{2} $ (Fig. 3-48). What is the vertical component of her acceleration?    $m/s^2$
(b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 335 m ?    $s$

  A basketball leaves a player's hands at a height of 2.10 7tkz+0cb1 ;o4tg 4ij6-6n flgqeiio8+ zw pfrm above the floor. The basket is 2.60 m above th;cgto fe8p4nlfq-1 6ior t0iwk jb+7zz+6g i4e floor. The player likes to shoot the ball at a 38.0$^{\circ}$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22 \mathrm{~m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves thwy4su h47)a .h(t kixse end of a $5.0-\mathrm{m}$ -high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine
( a ) her initial velocity, $ \overrightarrow{\mathbf{v}}_{0}$ ,    ${ }^{\circ} \text { above the horizontal }$
(b) the maximum height reached,   
(c) the velocity $ \overrightarrow{\mathbf{v}}_{\mathrm{f}}$ with which she enters the water.    $^{\circ} $ $\text { (below the horizontal) }$

  A stunt driver wants to mgqohr7oeq( 0qmy *o7:ake his car jump over eight cars parked side by side below a 7qogoo q:mery7( 0 h*qhorizontal 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 ,2.iflxavk b5lpo g 0,a)rp8f bat 0.90 m above the ground at an angle o2kfovpabr,l5,a8 . )0fxgiplf $61^{\circ}$ 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 with an initk-ma( wpw;1ez ial 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 building with an initial jcqyf7dqbom8( 97w:ar bx-- g 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 bei 4iai. kz2 hz3z0wtn6yng a 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 ho4zi06y. w 3k ai2htnzzrizontal range of your gun?