One car travels due east at and a second car travels north at Are thei7i) c p6-es s/imp(feyk; ,xgkr velocyg7 ke )i/-k p(,msp;cf i6xesities equal? Explain.

Can you give several exa6gv zasp1j2w)mples of an object’s motion in which a great distance is traveled but the dia 2sv1p6g) zjwsplacement is zero?

Can the displacement vector for a particle moving in two dimens)79 b7i ;vygumjgjmn8ions ever be longer than the length of path traveled by bgy7i8 ;n9jm) 7u gmjvthe particle over the same time interval? Can it ever be less? Discuss.

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

  Two vectors have lengt p;oa(.vbf wd0o+j .lch $ V_{1}=3.5 \mathrm{~km} $ and $ V_{2}=4.0 \mathrm{~km}$ . What are the maximum and minimum magnitudes of their vector sum?max =    min =   

Can two vectors of u a6f3m/q1n.w o6c bwscnequal magnitude add up to give the zero vector? Can three unequal vectors? Under what conditions /s36qn6a bccw mw1f.o?

Can the magnitude of a vector ever (7al1 x5moco( na) be equal to one of its components, or (b) be less than one of its c71 ol5noaxcm( omponents?

  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 first he/r my. rn q9(,cye(arop onto a moving walkway and then onto the cars themselves. Why iee(qr.ra,( my nr9 yc/s this done?

If you are riding on a train that speeds past anouj:78:bd2oeffu-xu wfc k1 h :ther train moving in the same direction on an adjacent track, it appears that the other train is moving backward. Why? d8 xb- uu1::wfc7 k:hoj2 fuef

If you stand motionless under an umbrella inn4t a+; z/te hlh-ekz7 a rainstorm where the drops fall vertically, you remain relatively dry. However, if you start running, the kh e+ n7thze4/t-azl;rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed ir bvuxg5k3j n793p+ktrain car, moving at constant velocity, throws a ball straight up i 5rk9b3p7gu3x+vjnki nto the air in her reference frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row at theysb t6 2o:c6xd same speed in still water, set off across a river at the same time. A heads straight across and is pulled downstream somewhat by the current. The B t: cbsdx6y6o 2heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baseball player “judges” the flir66 wwlx( gh;lght of a fly ball? Which equation in this Chapl6;6rw hgl( xwter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the ta lmv e71o7fk: bagfl )9bxa.m9rget? How should your angle of aim d9bmfa gblm 7)9a.k1 fev7x:l oepend on the distance to the target?

  A projectile is launched at an angle ogso4c+xsrq;8 5hqvxodc15 :c f $30^{\circ}$ 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 thety5hi9y+gc n1sj2a;xc6t+h k ground with identical initial speeds, but wijt gtxyk+1cyash96 h 2n+ 5ic;th $ \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 kglmc2zs;e81i:u8v f;gm* okis the displacement of the sgoe8;:mu 2 gvikz8m;lf1 ck*car from the point of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 2y+.tsbd o+gp x41tdwx8p.vh blocks north, 10 blocks east, and 16 blocks south. What is its final displacement from theo++gdbpttx.v2 p8dy. s1w 4h x 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 u,tiou9f(x zah y55rf62v9tmthe resultant of the following three vector displacements: (25f5i y 9vuao tfmt z9h6ur,(x1) $ 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 vwl9pnf:8 q5rt ai.gy:zlx1: uector $\overrightarrow{\mathbf{V}}$ 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 traveliy-rx; lws2 9zqng $735 \mathrm{~km} / \mathrm{h}$ 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. belowl :2sm.+;ghb04cagtufes xz 5f5h jn5. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give thsu+5h b:ml5 n0ghc x.j a gzf425e;tfse 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 vector8cazex,0lq;xnd d09ke- tc 4p s $ \overrightarrow{\mathbf{A}}$ and $ \overrightarrow{\mathbf{B}}$ shown in Fig. below , determine $\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}$ . (b) Determine $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}$ without using your answer in (a) . Then compare your results and see if they are opposite.


$|\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}|$ =   
$\theta_{B-A}$ =    $^{\circ}$above -x axis
$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|$ =   
$\theta$ =    $^{\circ }\text { below }+x \text { axis }$

  $\text { For the vectors given in Fig. 3-32, determine (a) } \overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}} \text {, (b) } \overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{C}} \text {, and (c) } \overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}} \text {. }$




$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$ below +x axis
$|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$
$|\overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|$ =   
$\theta$ =    $^{\circ}$ below - x axis

  $\text { For the vectors shown in Fig. below, determine (a) } \overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{A}} \text {, (b) } 2 \overrightarrow{\mathbf{A}}-3 \overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{C}} \text {. }$



$|\overrightarrow{\mathbf{B}}-2 \overrightarrow{\mathbf{A}}|$ =   
$\theta$ =    $^{\circ}$ below - x axis
$|2 \overrightarrow{\mathbf{A}}-3 \overrightarrow{\mathbf{B}}+2 \overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$ below + x axis

  The summit of a mountain, 2450 m above base camp, is measured on a mapm5xur;kf3z*7 gu. rjgn0dz)w*zxd t: to be 4580 m horizontally from the camp i u7gtj.wn:0 z*)*fddu m z;xxrr53gzk n 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 xys9ombzjh(bj .t*n aa 8ne7cd fa1e+(8 plane that has a magnitude of 70.0 units and a y component of What are the two possibilities foe z9s*antcabbfjn (8h( jeao+8.md 71r its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-hx54dj mof) )cfigh rock with a speed of How far from th4)m cf 5o)jxfde base of the rock will she land?    m

  A diver running dives out horizontally from the edrn ls86 i5/btzm:ldj:bn as1 -ge 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 diver :milbt1 bns5l /jrd:z-68snahit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water at a speed of cv2h4))axw0zt5bw hh1v cb+s At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are tw 4c+)zsw vv 0 x1ch)ah5bh2bthere two different angles? Sketch the two trajectories.

  Romeo is chucking pej,m9 gna2bvh*h; ;i9 tq9qdgxbbles gently up to Juliet’s window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the peb9 gi,tjxbm;a2qg* q9v 9nhh d;bles going when they hit her window?    m/s

  A ball is thrown horizontally from 9tc. -ncln5uv the roof of a building 45.0 m tall and lands 24.0 m from5 v-cnlcn9t. u the base. What was the ball’s initial speed?   

  A football is kicked at ground leve0 i mk4qgp/f+ho ptw7j 2-.rgul with a speed of 18.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at from the ro ei 8i.lkf+5*saz leo3of of a building lands 36.0 m from the base of the buildse3z .ofk 8i* eill+a5ing. How tall is the building?    m

  An athlete executing a long jump leaves the ground at a 28.0k0f :9 /dn95/rfvc 4oqecfabf$^{\circ}$ 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 txvq/oafj j)rw,- ;c qu,9m7oi he Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moon is onowr ,7a-muc f9qj x)/jo, q;ive-sixth what it is on Earth.    times

  A hunter aims directly at a target v (j9fduv j2:f(on the same level) 75.0 m away.
(a) If the bullet leaves the gun at a speed of by how much will it miss the target?  
(b) At what angle should the gun be aimed so as to hit the target?    $^{\circ}$

  The pilot of an airplane traveling wants 73mmplxrs9 hj13jsy9p n) h8ato drop supplies to flood victims isolated on a patch of land 160 m below. T 8x h73 jm9pm9jhsral1p3) nsyhe 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 initia d/u0yvk 67pm6l-noc; rz di*2,i4mzvvz5 vrml speed of at an angle of 34.5$^{\circ}$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot 5-(1m aedc vuofrom the edge of a cliff 125 m above ground level with an initial speed of at an angle of vc 5-md1euoa(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 u7ik *bjvgb/- ;*se4f,nw ytyan initial speed of 15.5 $\mathrm{~m} / \mathrm{s} $ at a $ 34.0^{\circ}$ angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 m above the ground.   

  At what projection angle will th whk69w3 obl,ne range of a projectile equal its maximum height? w3ko9 wl ,nb6h   ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the ;x ld4 wdj3gv0slingshot 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 bdl gv 0xwj3;d4oy 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 i oeh07bxjxa )jbb 2x dao2380wprk57isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with aj3ow2hrbb idpbe)xx o 700akj 2xa587 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 moaiu )ji xa q)q-3 dgj5fyk,) hvthf50/rning jog on the deck of a cruise ship is running toward the bow (front) of the shi)qf- hj3gh va 5)u,ta/iqyd5ji xk) f0p 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 chbq i( +e6v w0qmb)x(speed 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 09d 31hkhdpvhxtwy./ 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 2.3ai-g1zs9x ;7gobo b6m0$ \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 aifoxei *a6;4h speed of and they spot each other whehi*fiax; 6 4eon they are initially 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is heading due somv2(ve9qsqjas;sp -2 uth at a speed of 600$ \mathrm{~km} / \mathrm{h} $. If a wind begins blowing from the southwest at a speed of 100 $\mathrm{~km} / \mathrm{h}$ (average), calculate:
(a) the velocity (magnitude and direction) of the plane relative to the ground, and    $^{\circ} $ east of south
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.   
[Hint: First draw a diagram.]

  In what direction should the pilot aim the plane in Pq*dshd ,yw; wnx2t5 6+xk l5tzroblem 41 so that it will f*dww2d xs x,yqht tk;n+6z 5l5ly due south?    $^{\circ} $ east of south

  Determine the speed of the boat with respeci :k9,y) n awgij)jzta:t1 1ogt to the shore in Example 3–11.   

  A passenger on a boat moving at 1.50 k9m4vkt3zvk4 7x kod6w zm,(f$ \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 inxigl:sq: vxx: e w+isx ba-0-6 still water is 2.60 $\mathrm{~m} / \mathrm{s}$ must aim upstream at an angle of 28.5$^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current?   
(b) What is the resultant speed of the boat with respect to the shore?   

  A boat, whose speed in still wmy;zk0kx h(c7 (i xilebhm5 u)a6d j*8ater 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 s6sw((2:p fd d6 wsjdqof swimming 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?   
(b) How long will it take her to reach the other side?   

  A swimmer is capable of swimming zho- g3hbf,9i9 tnh:0 ec om(o 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?    $^{\circ} $
(b) How long will it take her to reach the other side?   

  An airplane whose air speed is0ppgc xw2t54 x po2;a7ti8ycb 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 a ccc dv 9/zhaneyyp1**+onstant 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.do18 rpws1hqq r )+/qd If the police car accelerates uniformly as given above, and overtakes the speq+rq) h/18wdro dps1 qeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a s7ur n(z f8m/jktreet corner at right angles to each other (Fig. below). Car 1 trave 8zurk(/7fj mnls at a speed relative to Earth $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , and car 2 at $v_{2 \mathrm{E}}=55 \mathrm{~km} / \mathrm{h}$ . What is the relative velocity of car 1 as seen by car 2 ?    km/h    $\theta$$^{\circ} $ West of North
What is the velocity of car 2 relative to car 1 ?    km/h    $\theta$ $^{\circ} $ south of east

  William Tell must split the apple atop his son's head from a distance of 27 7m 6vylbk f+0om . When William aims directly at the apple, the arrow is vmk0 yfo+l7b 6horizontal. 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 then tj+-8c ehrqyv -akes an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacev8e qr+c-h-y jment 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 +jtc:qw )ohfz 7e,v4 sroads, escape routes are sometimes placed to the side of the road for trucks whose brakes might fail. Assuming a constant upward sje)q t zw7fhc+s: o,4vlope 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 w2+ gu tunh41q(cxh,x y 2mxc)is 88.5 w(1hxxuc,gn m 2yh2+)c4 xtquand 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 angle -0g. b: rnc- j;dlg(zqo/vv th $\theta=30^{\circ}$ 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 spe(l3z oo)j1k il t0*ziked 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 nh,,97bbsbybd 6, uut$\mathrm{~km} / \mathrm{h}$ passes a 1.00$-\mathrm{km} $-long train traveling in the same direction on a track that is parallel to the road. If the speed of the train is 75$ \mathrm{~km} / \mathrm{h} $, how long does it take the car to pass the train, and how far will the car have traveled in this time? What are the results if the car and train are instead traveling in opposite directions?

  An Olympic long jumper is capable of jumping 8.0 m . Assuming his horizos nm-s n +*nlr5v:am4k)s ac5vntal speed is 9.1 lmnv 4 s-5*k rvama):ns+snc5$\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 ball about 180 fa o ;-sdln(h().xobu m! Assuming that the swing, launch angle, and so on, were the same as on Earth where thefodl ;ob-anhu)((x . s same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer ovej6q sg-c7 0-qypbn ne7r 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 platforms abouteg *ciaa1n x):*j g0ls 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 to clear the roas 0n1l*gx*gc)ji ae:cks?    How long are they in the air?   

  At serve, a tennis player aims to hit the bld3b op2(futp))q8x iall horizontally. What minimum speed is required for the ball t)bpi xodu8t)q 2(lpf3o clear the 0.90-m-high net about 15.0 m from the server if the ball is “launched” from a height of 2.50 m? $\approx$    Where will the ball land if it just clears the net (and will it be “good” in the sense that it lands within 7.0 m of the net)? How long will it be in the air? $\approx$    See Fig. below.

  Spymaster Paul, flying a con 3d:tu..ydg hkstant $215 \mathrm{~km} / \mathrm{h}$ 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 boam tghv)nm+65it is to make a round trip in a river whose current travels at speed u . Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving (a) upstream and back downstream, (b) directly across the river and back. We must +g6m5 mv)nith assume u

  A projectile is launched from ground level to the top of a cliff whilly8pc 92m;;8p7c8cpqtqnsz; l3d gu ch is 195 m aq7 z 23u9csplclm8t ;c8pgql;n8dp;yway and 155 m high (see
Fig. 3-47). If the projectile lands on top of the cliff 7.6 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance.



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

  

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

  A basketball leaves a player's hands at a height of 2.10 m ab .m q+x(ielpg/ove the floor. The basket is 2.60 m above the floor. The player likes (q ei+/xlm. gpto 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 enspx.v- kc4ud/ d 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 wantsm5hhie ;14u+fe ay /5 kazrev6 bnf:nk5sj+(y to make his car jump over eight cars parked side by side below a hor f h n++ rum65bk/y1zef h4ia5:yvase(e5 n;jkizontal ramp

(a) With what minimum speed must he drive off the horizontal ramp? The vertical height of the ramp is 1.5 m above the cars, and the horizontal distance he must clear is 20 m .    $m/s$
(b) If the ramp is now tilted upward, so that "takeoff angle" is $10^{\circ}$ above the horizontal, what is the new minimum speed?    $m/s$

  A batter hits a fly ball which leaves the bat 0.90 m a;-k8gzdxpzb w.wxr pp,t9 9t. bove the ground at an angle ofp pw 9.z- xkzd9;brwx. 8,gptt $61^{\circ}$ 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 initial speed o4rbk+s-; zrpa1,e uhmd 4fv8 g ;qo2rpf $32 \mathrm{~m} / \mathrm{s}$ 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 initiasbm u c3huh-kkr0e59/ l 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 physg rnvty)*w5 l:ics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, wr l5*)vgty n:and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?