One car travels due east at and a second car travels north at Are their )jmne+1 i /son- mjd2cvelocities mj- c +omin2s1end/j)equal? Explain.

Can you give several examples of anau65hi mwlx1p/, c)dw object’s motion in which a great distance is1w,)xlwuhp d56aic/m traveled but the displacement is zero?

Can the displacement vector for a particle moving in two dimenst4r d1dl5nbbj2 ; rtu-ions ever be longer than the length of path traveled lr5u42tj t1 bnr;d b-dby the 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 lengtzsu lnt. 6j;6lh $ 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 pcj9a/ adkg iuk.3 /k5add up to give the zero vector? Can three unequal vectors? Under what coicjkkg 9p3/kadua/ .5 nditions?

Can the magnitude of a vector ev5jft; kni: 9p1hai-bb i rs;y:j 20dvrer (a) be equal to one of its components, or (b) be less than one ofbit2f rh5-k9rj; n:0v pbdi:aysj i1; 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 first hop6+vm (/ 0lqj0s:q 2bzbund f-yhw ypu+ onto a moving yh0(2bw:sqm /6-plu nu++ zf0v qjybdwalkway and then onto the cars themselves. Why is this done?

If you are riding on a train that speeds pasthn9r2 baw);xe another train moving in the same direction on an adjacent track, it appears that the other train is movin hn 2x;ra9ewb)g backward. Why?

If you stand motionless under an umbre8,rru8 yp0we 6rzwr 5plla in a rainstorm where the drops fall vertically, you remain relatively dry. However, if you start running, the rain beg wwy,5u8rr8ep0 6zprrins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosedzfkkvw0+kr(;,azb 3 l:j p qe7 train car, moving at constant velocity, throws a ball straight ulj73 vzak0bef:kqk+, w; (pz rp into 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 the same speed in still water, 4;lrnfu-ydnlr np;d*;xxkk. 96 n8 tzset off across a river at the same time. A heads straight across and is pulled downstream somewhat by the current. The B heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reaches the dr89-knxrnn4 .yx ;z;fldpk* ;t 6ulnopposite side first? ----待选择----AB 

How do you think a base nj8fepmii f5)wx+ ;91nts:xgball player “judges” the flight of a fly ball? Which equation inij;i: sxfnn95e)gtf1 x8m+pw this Chapter becomes part of the player’s intuition?

In archery, should the arrow3wbedfw/h/rdh3,cs pd o0wb6;eg o/0 be aimed directly at the target? How should your angle of aim depend / wp3w0fgd/ 3b6bhod,r hcewos 0d/ ;eon the distance to the target?

  A projectile is launched at an anglt1 d 4x2s+rhpie 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 fr.* n0viut0 z-9+ fckhbjizq*yom the ground with identical initial speedsj fhniq czvz b t9*.-y*0u+0ik, 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 andn l)s/6 kmb0qj then 85 km southwest. What is the displacement of the car from the poinb0 lj6n)qsm/kt of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blogglqwd+akvj ( qu/; k,hg .-t9kh5;cucks north, 10 blocks east, and 16 blocks south. What is its final diq /g ; 9khqw.c+dt; lkj,(uhakg5g-vusplacement 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 r7oqel o7yd8bz1gwx p r +2y8c5esultant of the following three vector displacements: (1) 7qwx7g ly8bed5cro2yz p o1+8 $ 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 vectorj 4 llp5srpm 9j tk5eu)e8r4*p $\overrightarrow{\mathbf{V}}$ 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 (l2df8fyeej,. * uulbing $735 \mathrm{~km} / \mathrm{h}$ 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 inn2c. 1 ug 4(hi;ydfafqln y8e* Fig. below. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in.lhi;(fyne18 2 dugqy4 * cafn 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 vector4mj w+t+yvj v8s $ \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, 2xbm( hd,z ka1 *c.kkt,450 m above base camp, is measured on a map to be 4580 m hori.,a1mxkdk zkhbc( t*,zontally 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 th0a w r uwfl1,w;+w2lkbat has a magnitude of 70.0 units and a y component of What are the two possibilw ,wk 1l;a2f0b rwwlu+ities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with h lwf0w6fi1 -la speed of How far from the base fihl lw6wf1 -0of the rock will she land?    m

  A diver running dives out horizontally fwy91amts 1rxyos 0 6g )wpor)0 z3u9ptrom the edge of a vertical cliff and 3.0 s later reaches the water ax 3o y0s)1r6y19st p mwgpwt9or0uz )below. How high was the cliff, and how 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 z/7cy8nz j aqffw-0nf i j(z2;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 twiz / z;ywfj87 - a2nfqcnz(j0fo different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Jne:wcjd-y b);uliet’s window, and he wants the pebbles to hit the window with only a horizontal comd) cj ybwen-;:ponent 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 her window?    m/s

  A ball is thrown horizontally from the roof of a building 45.0 m tall and lands ;pd 4:t .t4a6put,xcgehrz9 z 24.0 m from the base. What was the balhp .zc:t 4t r ptx,;6d9zu4agel’s initial speed?   

  A football is kicked at ground lev0vl. lq9ub( snl:6bgp el 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 n ) a;c(*v,*oohwhgx(ccc i, v from the roof of a building lands 36.0 m from the base of the building. How tall vn x* ho)cwg(cc h(v,, ia;c*ois the building?    m

  An athlete executing a long jump leaves the ground atv7 dyk,xhwo3 sx2 k17o 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 Moon as compared tolfrx ho lspc) t2 -z/s(ywl/sec6 +.k4 the Earth if the takeoff speed and angle are the same. The acceleratio kl r2h+ ylsclexso4(t cpfzs/). -w/6n due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 754 +tdm:qgmq(1 kta mq:.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 fl2d xtf d/ r,v;cge/8mlood victims isolated on a patch of land 160 m below. The supplies gd;el,/m d cxr /2ftv8should 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 initial1mub ;otiur.2(2cuw j 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 from the edge of a clskml90 n 5:qfxiff 125 m above ground level with an initial speed of at an angle of 37.0º with the horizontal, as shown in Fig. be m90 5sqlx:kfnlow.
(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 withqa0 *d: eyw :i8hj:uzwbks4:q 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 j tnkc jp*20rzz/,i1f equal its maximum height? kj pc/*i1tf 2zj0zr,n   ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the slingshot i whrqu10ndj1. s below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that 0 ur.dqnhwj11again 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 mountain climbeq+t7btlvv )lg1 k1 dr1rs on a rocky ridge 235 m below. If the plane is vkl )gvtt1brd7ql 1+1traveling 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 th(8(jttai w;v- kg/s)q g:ur tce deck of a cruise ship is running toward the bow (front) of the shwtg(/gv-atkc is:q8)rut ( j;ip 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 speeda(pwu2yni2 3i 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 gmr hm75soi9;fxm.j j+2l2qmhighway 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 2.3t+jwxeok:* . b0$ \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 headm:,h/sa h bo kj7gkyoa0od; t7wty * ,grm9)1f-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 )ktm gda/roo9,j7k hwg a o,*7f0s;mb hyt1:y to take evasive action?    s

  An airplane is heading due soud mg331he .(doi+lt omth 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 4dgc 7nc:;, p g -4 v9xdv7pd.kssibpbthe plane in Problem 41 so that it will fly due so7cn s;, -cdx79p.pi gbpb skvg:4d d4vuth?    $^{\circ} $ east of south

  Determine the speed of the boat with resu.8hz v o63vetpect to the shore in Example 3–11.   

  A passenger on a boatgy9v odv msb2y8*.e8b moving at 1.50$ \mathrm{~m} / \mathrm{s}$ on a still lake walks up a flight of stairs at a speed of 0.50 $\mathrm{~m} / \mathrm{s}$ (Fig. below). The stairs are angled at $45^{\circ}$ pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?   

  A motorboat whose speed in still water/l5db vw /q 24 mzdq kmj9p.fkpp).t*p 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 sb/p.2x0japhm mle, 4 ftill 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 swimminraep2/q5 fu h:g 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?   
(b) How long will it take her to reach the other side?   

  A swimmer is capable of swimming 0.4fqnkwa0 7e 2cdci8q6kp tw2235 $\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 62vktcb8 )f431ln, fr3ufi qv 41uzcj7t 0$ \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 con92b ci; g.vffdstant 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 k-j b 1 f79mhc4puj0osvnown. If the police car accelerapcs0 - vmhoj7u4j b91ftes uniformly as given above, and overtakes the speeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner at right angles to each other (Fig. be0l*ufs. zcab11dkw g. low). Car 1 travels at a speed relatau1gkf0. *cdz lwbs. 1ive 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's7 ix z,j888zk.ms a epyj,y.vg head from a distance of 27 m . W j, sgzzyey 8kp7i..m8x, 8vjahen 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 of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east8vig( vszt p3m 70.cwl and 25 m south, and then takes an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Gv7083zvw.ci (l mtg spive 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 placed to ts,qw 2n.-/xme yx; mckhe side of the road for trucks whose brakes might fail. Assuming a constant upward slope of m;2 e qs,nkmxyx.wc/- 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 componegqj lce; mk5rv9qdz 3 y* )9rzllv+2s;nt of a vector (in the x y plane) whose magnitude is 88.5 and whose x component iygzsrllvj q3)c v 2*+e9;9krq;zlmd5s
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 anglekp6 -plgf53+-wgxs 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 d)ud*y7mf)+im+r yie5xy tj4d ue south with a speed 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 1qjn;(1* p dht5cvw+um 7ox + 9rwz* iwitk0pq$\mathrm{~km} / \mathrm{h}$ 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 . Assud- tiwe6 m96ucming his horizontal speed is 9.1 itew6cmud- 96 $\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” topq w+xj2 n5g0z 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. (Neglect air r2qj+ g xzpnw05esistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homerq9j-shqge;zi9j* tc+c oq w*/ 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 he 1 hd(zwvenx21*(p)ngj 1ynpush off horizontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point.h((j12pzn) n1n egvhwd1 *yex 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 b fvcl21/;7ibuci8t9jday iplq 5 --otall horizontally. What minimum speed is required for the ball to clear the 0-qi8 lut pi2i5-b tl;1/7ydfccoj 9av .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 4qs7cabc cwdf:) d /-ua constant $215 \mathrm{~km} / \mathrm{h}$ 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; acjxxy lop 0t 9m85mtz2xjk*acp: 98 make a round trip in a river whose current travels at speed u . Derive a formula for the time needed to make 5 xtp:9c k 2z ;0mx889yoaatj jlmpcx*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 ground level to the top of a cliff which iscwfnppw;uxrli,l(p ;u1hi ( g) ;7b;o 195 m away andwi;;71cpglwpr ,b;upx ;f(i) uo( nhl 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 aboveqo6 rpd1to 1+40cpvkm the floor. The basket is 2.60 m above the floor. The player likes to shoot the ball at a oq1c4tpdm v6o+ krp0 138.0$^{\circ}$ 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 thp7ptye/z 3im0e 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 make his n/eopqeb.:dd7fd1 tu iwj 75vk,/e 6scar jump over eight cars parked side by side below a horizontesdpw k.1b nu,e :77qfdtodijv65//e al 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 mxl 49xri. a;2ro hi3ywhich leaves the bat 0.90 m above the ground at an anglexo4 9am;h xi.y 2rlir3 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 baseball with an initial spe bp5dfx i+s;ykv7 4h0xed 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 to ci) h4pqy *+/76ii qq9ffd6bqs6sokgp of a building with an initial velocity of 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart gun, and being a c 7xws 1heyfy ytni/b,e*3cyy q :n99i:lever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun strx*i3ey1bciyq/t :e nf hn 9 y9,yyws7:aight up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?