One car travels due east at and a second car travels north at Are their v:yf-;8h z thlvelocizf: hh-8tlv;yties equal? Explain.

Can you give several examples of an object’s mo 9-j,lczfty4 btion in which a great distance is traveled but the displa yfjt,zl4 b9c-cement is zero?

Can the displacement vector for a particle mrn(ew ms zm(ye/e, ,bnu1iq88oving in two dimensions ever be longer than the length of path traveled by the particle over the same time intervalen mer1(w / 8z,8um(seiybqn ,? 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 lengti *1r51wzygvvn(l g.fh $ 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 awgtr 0wt wvdc.e*+1 o/dd up to give the zero vector? Can three unequal vectors? Under what conditions?.*0 wc ttgdw1rwo+ve /

Can the magnitude of a vector ever (a) be equa/ ,rj q5zq n;.y2vs/stjiinu(l to one of its components, or (b) be less than one of.(qn/ ri,ivj/ qzsun t ys;25j 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 rideqg:qwj- 3fx..y/qp7us vb a8ars first hop onto a moving walkway and then onto the cars themselves. Why is this donea/ u.x:f3qyp-7v8baq jw qg s.?

If you are riding on a train that hhszn x7*dg; 0speeds past another train moving in the same direction on an adjacent track, it appears that the other train is moving backwarhzn* s7dgx; 0hd. Why?

If you stand motionless under an umbrella in a rains0rd9 pz52lnos torm where the drops fall vertically, you remain relatively dry. However, if you start r052os rln d9zpunning, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train carv 5+huzw*yv w 5v w:(z*oceo2j*uwi1j, moving at constant velocity, throws a ball straight up into the air in her refer*y*zuuo2evvczwv+ wo5 w5 j: i1hw*j( ence frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row at the same speed in still water, set off acro itvve28fh a25a 0j,ydss a river at the same time. A heads straight across an 5je yf2i8atvh,dav20 d 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 side first? ----待选择----AB 

How do you think a baseball player “judges” the flight of a fly ball?+ s1 yg,k+c3 p+2hu e*h*t yrmjgy,dri Which equation in this Chapter becomes part y 3yit,2 hj gs,ruh1c +k*g+dy+re*p mof the player’s intuition?

In archery, should the arrow be aj x,12spc:8;pcwq l+v,vrzg qm1(pv p imed directly at the target? How should your angle of aimq:v,c,c 1gwmqzj r(xv 8 ppps;pv1+ l2 depend on the distance to the target?

  A projectile is launched at an angle of 5gsmbjdx *7/ e4 *xafq$30^{\circ}$ 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 , tr8v3vk/wjlaqg 5w/nwf:j40 are fired from the ground with identical initial speeds5/08a4vwg/fk r v3nltjwjw: q, 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 west and then 85 km southwest. What is the disb 4yh w/o07oujplacement of the car from the point of origin (magnitude and direction) jyo0/47h wubo? Draw a diagram.

  A delivery truck travels 18 blocks nort,c- qt7k*89ckojbuf lh, 10 blocks east, and 16 blocks south. What is it8,tfc- ou l9*k jkb7cqs final displacement 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 the resultant of the fg l)ue 8cq+c;ld2o q*aiz+t9xollowing three vector displacements:ixtdqc c)+o 9g al*q+2zelu;8 (1) $ 34 \mathrm{~m}, 25^{\circ} $ north of east; (2) $48 \mathrm{~m}, 33^{\circ}$ east of north; and (3) $22 \mathrm{~m}, 56^{\circ} $ west of south.

  The components of a vec t)l645/dr(sk6 hbn b biac+lqtor $\overrightarrow{\mathbf{V}}$ 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 travel;3k5o* pvjqubb nu(6 ming $735 \mathrm{~km} / \mathrm{h}$ in a direction $ 41.5^{\circ} $ west of north (Fig. 3-31). (a) Find the components of the velocity vector in the northerly and westerly directions. (b) How far north and how far west has the plane traveled after 3.00 h ?(a ) $ v_{\text {north }} $=   $v_{\text {west }} $=    (b) $\Delta d_{\text {north}} $=    $\Delta d_{\text {west}}$ =   

  Three vectors are shown in Fig. below. Their magnitudes a-9 hfy ca/8yjvre given in arbitrary units. Determine the sum of the three vectors. Give the resvayh j-/98c yfultant 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 4t;dt*w( nnd .iji8k( sa+ uzuvu2 i:r$ \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, 2y3/ euwknm.9;r e.1) 53f cfjzk mozxf450 m above base camp, is measured on a map to be 4580 m horizontally from the camk n/cr eofyu3 f.w.z)fm ex5 1mkj;93zp 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 pl0go; x s9bklty(+ q4gwane that has a magnitude of 70.0 units and a y component of What are thx g(+4qo yk;90 bsltgwe two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6 dxl6 re1p* 89,zpxdxv.5-m-high rock with a speed of How far from the base of the rock will she land? d1xvx98*pep rxz6 l d,   m

  A diver running dives out horizontally from the+xdrr3(5nd9hij af .x 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 diver hit the water? high of cliff id a 5+irnxhd (.jxr9f3s    the distance is   

A fire hose held near thectbjkn 1+ s07c ground shoots water at a speed of At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there two differ7 1jcn0ktcb s+ent angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to k01v(q)u zw5vjkh 0foJuliet’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). Hzq0kvv w) u( 1kj50fhoow fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontally fro1qx ,knd .cf*rm the roof of a building 45.0 m tall and lands 24.0 m from thx d*f 1qrk.c,ne base. What was the ball’s initial speed?   

  A football is kicked at ground level with a speeds3 k85no *6*,b zvyy:*c xeiy pyv)5fokxn v9a 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 la 69 lwgivpruj2s3;/ylnds 36.0 m from the base of /g 3 yl9;6uj lvs2iprwthe building. How tall is the building?    m

  An athlete executing a long jump leaves the groundt)h ub9 gx,vcab:ao -o81 l8lt at a 28.0$^{\circ}$ angle and travels 7.80 m .
(a) What was the takeoff speed?   
(b) If this speed were increased by just 5.0 % , how much longer would the jump be?   

  Determine how much farther a person can jump on the Mo+dlmnyki- ;j+on as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravd-lk+ ;m iy+njity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 75.0 m as,vhgtok2gj r3s5 o0 5way.
(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 tra-bc2vob 0bf 6bveling wants to drop supplies to flood victims isolated on a patoc6bb0-b v f2bch of land 160 m below. 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 ua/khv9+ 8r4;fzyhoca8s xc3 at an angle of 34.5$^{\circ}$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot from the edge of a cliff 125 m ax2oor(j c p,d5bove ground level with an initial speed of at an angle of 37.0º with the horizontal, as show,5rpjxdcoo2( n 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 witx-rck/w- mo jkj39dg*7ce(db h an 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 the range of a projectile equal itsvwdo8l i:w; d0 maximum height? iwd;o8lwv 0d:    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the slingshokp 5ju9)n(: ey 3 kp+gdw+ahfot 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 trh d9u )+nga(y5f:eokpk p3+w jee makes the wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants to drop supplies to isolatdyz5.zb wt *f3ed mountain climbers on a rocky ridge 235 m below. If the plane is traytd w3z b5zf*.veling 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 on the deck of a cruise ship is running to7og r q07junm te54vz/*n 7jxoward the bom 4onvu rjq/x7 nz*o70ejt 75gw (front) 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 speed of 8kk 9t,obspy 1 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 o83 w ky;qj8 wc2qcq5fyn a highway 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 2.30.yuyzl sa q,5/$ \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 headhj70pyibgr c (;xo t+4w:u9 2edew;xu-on. Each has a speed of and they spot each other when they are initially 11.0 km apart. How much time do the pilots have to ta;x pjieug 7y(e0+ 2d bo:htwu4xc;w9r ke evasive action?    s

  An airplane is heading due south at a speeaj*y b,30fvzvn1+ gbdt7 5fc2 tvdey1 d 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 pilottwo0im z5ri+x4882rx sibn f: aim the plane in Problem 41 so that it will fly due south? +25 tmnxi:x4ws0 zb i8i for8r   $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shore ifwj 91qgqc0 q; 1d;lhbn Example 3–11.   

  A passenger on a boat moving at e fz.h-z59wpn b2llh7vaooyhuz7ox3 *(yx. 0 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 st3ar x-jynp( a(qusf5h2 unr vg-75d5dill 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 water is 1.77jl-xy kuil .90 $\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 atrh q) b c5f80 qbuao,k5b(i90.45 $\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 od1c ws .0cpqx+)uhuklf3q6 9g f swimming 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?    $^{\circ} $
(b) How long will it take her to reach the other side?   

  An airplane whose air speed is 620orr1l qo io;9+$ \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 c5mck td.8tb9pn .8uwsar, traveling 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 peqr5h+, aq-ethe speeder’s speed is not known. If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what wa-qrea5h,+ pqe s the speeder’s speed?    km/h

  Two cars approach a street corner at right anglok/rl-xi2 a ea maes3exzo*o1+-.;ukes to each other (Fig. below). Car 1 trave-xkx ; -*zl3os/1oe.euiao+mk a r2a els 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 fr9(lorvf ae1 xrbxck)ym/7z; 7 om a distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed oe1)b7; oraxyc7(9fkvzm / r lxf 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25 m sokst h*p 0sn74 2tkxy4. gnlzb/uth, and then takes an elevator 10 mn /spstkgz4 n .2b ly0x4h7t*k down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, 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 sometimes plk/8;paetc 64boo- ooeaced to the side of the road for trucks whose brakes mobaot6 k/pc48;e-ooe ight 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 magnitubpvw tp0yd;du0csb- x. ) *u+ g9a/+csz.zpdgde is 88.5 and whose x component isgvdc */u pdx pspd..9ts+)0c+0ybw bg-au; zz
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.l2silc b1uh 3e $\theta=30^{\circ}$ 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 6sz16 1 8 arb7yagiosz 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 (sz cogkl+ u4)/pzkoqvmp16lb yu46,$\mathrm{~km} / \mathrm{h}$ 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 j a*3cyz.wfs1 m . Assuming his horizontal speed is 9.f3s c wj1.a*zy1 $\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 baln+rn exzy iae1rd,)wlnu n8.7g 3.i4tl about 180 m! Assuming that the swing, launch angle, and so on, were thene atg),nnl 3uy4ri8z.1end+x wr7 .i same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over th l jd;l+)ghv4we 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 of sys)vcxqzzv03 o8m*)f horizontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water lez c3)y)o sx0vvmqz8s*vel 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 h3z8arbnjbwa -zt nb+ 1 pe(0zj0 82hpbit the ball horizontally. 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 b3j 2pn j 80 0(pbza8aeb-hn+rbbw1zztall 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 coj5t(a efaqapkq. qd9 9nh*7hl25 woo0nstant $215 \mathrm{~km} / \mathrm{h}$ 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 wb;u (xcv-np2;if-nj(j y. mjk8hz/u in still water is v . The boat is to make a round trip in a river whose current travels atn b-k8;-j( cw2nufpy.jh ( / mx;zivju 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 assume u

  A projectile is launched from 2w r-g0p*p;km6k ukipf) 7wqmground level to the top of a cliff which is 195 m away and 155 m high (see 6w 2*- mwg)fiqpkpkr0pmu k7;
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 playe)-ua 8.zcau fhw. d*ngr's hands at a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The player likes to s -au*w hznf8. .cau)gdhoot the ball at a 38.0$^{\circ}$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22 \mathrm{~m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves the end of aq*jlkubc9 u.8d4f l d+ $5.0-\mathrm{m}$ -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 jump over eight cars parked+m )7oc+6 aj )9 p7guxwoyzp b6d+matk side by side below uk6y ztdo6 c aowp+x+pb)m)7+am7 gj9a horizontal ramp

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

  A batter hits a fly ball which leaves the bat 0.90 m above t1t g2x+,; . ambobixvuhe ground at an angli;a but ,x+ mbxvog1.2e of $61^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s} $ heading toward centerfield. Ignore air resistance.
(a) How far from home plate would the ball land if not caught?   
(b) The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level.

Find his speed.   

  At t=0 a batter hits a baseaw: dxg5p*hz)w ;:kba ball 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 o7 e-asei;0tl ef a building with an initial velocity of 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart gun, and being a sne9 m1 y8.ry3qf tf-jclever 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 ba 3y1rtjeyf8nmq - .sf9ck at the barrel. What is the maximum horizontal range of your gun?