One car travels due east at and a second car travels north arw+7z1glwwzoq: xtc j .4cr+1t Are their velocitiesr1:+ cxj+g q t4ww.colzrz1 w7 equal? Explain.

Can you give several examples of an object’s motion in whicc/mvc v-.e *x-)pxrmzh a great distance isxrvc -p*-z /xvmcme). traveled but the displacement is zero?

Can the displacement vector for a particle moving in two dimensions evun9) rbc8;h ak/ 2hu15jz o.w 2hlhhmper be longer than the length of path traveled by theu wpuh 5z/h2. jno2) ha9hr;l8 bh1kmc 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 leng1(7am ;nyam 5eldtge/th $ V_{1}=3.5 \mathrm{~km} $ and $ V_{2}=4.0 \mathrm{~km}$ . What are the maximum and minimum magnitudes of their vector sum?max =    min =   

Can two vectors of unequal magnitude add up to give the zero )ij7 vzy9f:m rt *gdw7vector? Can three unequal vectors? Under what conditiy r t9:dg mjwz7v*)fi7ons?

Can the magnitude of a vector ever (a) be equal to ojc y.3e/hop/g.:9q 5g3v atvmp qwuf1 ne of its components, or (b) be less than one of its componentuye/govg3 5jcqf.3 q 1v9ap m/wph.:ts?

  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 firstt wz--ph519alr jse;u hop onto a moving wa5a-h lje urs 1-9tp;zwlkway and then onto the cars themselves. Why is this done?

If you are riding on a train that speeds past another train moving eo/mlg ouvr7tsky+k- -p7e)4 in the same directio4v 7-p+o-/e7etrykogkm)u sln on an adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under an umbrellcf oq 73 vl8)djpoxb02ja, 3gda in a rainstorm where the drops fall vertically, you remain relatively dry 8d aqj2x7bfo vjg 0o3l3d,cp). However, if you start running, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at constant velocity, throws a8 bs0iwo :fw9tunxihaa6im,;38 g/b w ball straight up into the air in her reference fr wanouibfbh9m/aw gw,0t ;36i8s: i x8ame.
(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 sameehu2 c - 5luw+0j5vep,ua-v yx speed in still water, set off across a river at the same time. A heads straight across and is pulled downstream somewhat by the curru au e-,u20hxv wjpe5l -5yc+vent. 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 “j hmo(w,ar h3fh ro3(2zudges” the flight of a fly ball? Which equation in this Chapter becomes part of the player’s intuition( ho2o3a(zfh3r, wh mr?

In archery, should the arrhp+u ;8x 2lxmj;gdom4ow be aimed directly at the target? How should your angle of aim depend on the distance to the lh8;dx;pjm o+gx um24 target?

  A projectile is launched at an a0.y)okrb8pt qngle of $30^{\circ}$ to the horizontal with a speed of $ 30 \mathrm{~m} / \mathrm{s}$. How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch?   

  Two cannonballs, A and B , are fired from the ground with idi; k x1j :f34wcvfkl,ugh (3huentical initial speeds, lwjgvi(1k :hc43 uxf; u kfh,3but 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 sout*i0,s 6tn,n w) x3 :iuf)pnqzdm5hn p9hahe/ zhwest. What is the displacement of the car from the pofnnh )hxnpume50:3)dai, /i tnzwh6 9,q*pz sint of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 ;c :tal g,zjbrwto,f*6 x a:x.blocks north, 10 blocks east, and 16 blocks south. What is its final displacement from the origin,6 wxl*x ;at.f g,: :zocbtrja? 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 following three vector displacementsocuf-mg3 ,h d;jk5ap5: u-m5 jp 3dka,ocgh5;f (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 ve24 9a-lo,+pqxiv nh njqmf 76octor $\overrightarrow{\mathbf{V}}$ 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 travelingzvv 0s k-t*2tz $735 \mathrm{~km} / \mathrm{h}$ 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 are given in arbiaqg hslfgv (5l+ pe)-)9vd0ndtrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with the x a0)a-(v)pg v5esn +q9llf ddghxis.


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

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



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

  (a) Given the vectors xqi4e.g2z*qqhguo 6z,)i0f z$ \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 cam8d. ;sk qti1ik6 xky;rp, is measured on a map to be 4580 m horizontally from the caik qx;;s6d1itk. kyr8 mp 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 inbae9twvxs 9 1ns jhzowo r.)59 a0fr.8 the xy plane that has a magnitude of 70.0 units and a y component of What are the two possibilities for its x componento wjs af) wexza1bs59.v.9o89rth0rn? x = $\pm$   

  A tiger leaps horizontally from ae 22y0xgp6 um3 renb9g 6.5-m-high rock with a speed of How far from the base of the rock will she9mp0egu6ygn2r x 32eb land?    m

  A diver running dives out horiz wc3 f,f * zygbhon3k3o/8oapb7.vtc4ontally from the edge of a vertical cliff and 3.0 s later reaches the water below. How high way3hfwf z/,aobk .cnv8cbp7 t4 o33*o gs 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 a speed of At wh(, v lbilf3abxw56zt5 at angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch5 f( 5lz6ab,3vt wblxi the two trajectories.

  Romeo is chucking pebble-* f9rw,q 1qjbgmxk)zs 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. z *fg)wk q1-,jmbx9q rbelow). How fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontally from the roof of a ;o6 .j 3ul w,ffav4o8wy.xkba building 45.0 m tall and lands 24.0 m from the base. What wao8v.xfwu;4oaayfk.b 3lj 6 ,ws the ball’s initial speed?   

  A football is kicked at ground level with a speed o.7e1d:k r.at)mgk tns;cu-k ff 18.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at from the roof of a building lands 36js7v s3,;xl1u q)ck+cx ur:b j.0 m from the base of the builduxjks 1+lxuq3jbc,)sc r; :v7ing. How tall is the building?    m

  An athlete executing a long jump leave:1wnmf qk0z e/s the ground at a 28.0$^{\circ}$ angle and travels 7.80 m .
(a) What was the takeoff speed?   
(b) If this speed were increased by just 5.0 % , how much longer would the jump be?   

  Determine how much farther a person can jump on the Moohz8sc31 2 ht05lbcup pn as compared to the Earth if the tak0zlp3 8t hpu csh5b12ceoff speed and angle are the same. The acceleration 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) hyps /;;eit nlc)+1+logkmh 175.0 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 fl0tswx8 9z.v1c-bhe 2zrud u 8vood victims isolated on a patch of land 160 2tvzzd u 1b-8hus9xcr e08 wv.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 wit2 ngy;3)vmxdiwg9 5ehyt4ztpjl 4 (q,h an initial 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 cliff 125 m above ground level with ai ,hqlitqf 5,0 luij* ;m4mn8/k6qnue n initial sp k5tum0qif ihn,/8;l 4mi j qq*l,ue6need of at an angle of 37.0º with the horizontal, as shown in Fig. below.
(a) Determine the time taken by the projectile to hit point P at ground level.   
(b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find   
(c) the horizontal and the vertical components of its velocity,   
(d) the magnitude of the velocity, and   
(e) the angle made by the velocity vector with the horizontal.    $^{\circ}$ below the horizon
(f) Find the maximum height above the cliff top reached by the projectile.   

  A shotputter throws the shot with an initial speed of ,ehrb fv5 :i9s:nizw; 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 equalyonhrv :b zvk) t ny)s:x;j04tgw+ +8;ctxt8p its maximum height?;nzkxtwn b4;vh):t8c :g yrv )t0yps+o+8x jt    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the slingweu b/ 8.xmogo,wj: k)shot 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 wwo e: kmg j).ux/8,obin the tree makes the wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants +,x5* orl eyzbto drop supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with a spe boz5l *+exyr,ed 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 u2 cr0)fjja( hship is running toward the cru(j2 ) af0jhbow (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 0. ,h*jaz).cm fl60$ \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 highwaxiv (axdon6s;p9u( b9 y 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 2z1bv/,bexd :f 6i6bhf+kbvp) .30$ \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 a6k;t lbc tb-3a speed of and they spot each other when they are initially 11.0 km apart. How much time do the pilots have to take evasive btbl- t;a6ck3 action?    s

  An airplane is heading due souftr z2)zrasmpvi *6d:tt aw 6tz18t8 .th 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 Problem 41 so thaa+ 5iccjbv:r. t it will fly due s.5c: vbirja+c outh?    $^{\circ} $ east of south

  Determine the speed of the boat with respectee6+pq),efu t to the shore in Example 3–11.   

  A passenger on a boat mo emn) ziqx9 6jsm7i.a )9b3a0 cnol;qbving at 1.50$ \mathrm{~m} / \mathrm{s}$ on a still lake walks up a flight of stairs at a speed of 0.50 $\mathrm{~m} / \mathrm{s}$ (Fig. below). The stairs are angled at $45^{\circ}$ pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?   

  A motorboat whose speed in still water is y 9 3l9hg5z dmw(+wguo2.60 $\mathrm{~m} / \mathrm{s}$ 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 fb:)p7az,la/ b utwc5 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 capablef0k3f y d25o+te feke6 of 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 0.45 +lnhs :sw 058p8wcz4yx; jb uatd13gc$\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 aov/)v((ofyv:m,jw g y(8z,, xctol f620$ \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, tre bq4nccxw+i94c +h 6waveling a constant 95$ \mathrm{~km} / \mathrm{h}$ , is passed by a speeder traveling 145$ \mathrm{~km} / \mathrm{h}$ .

Precisely 1.00 s after the speeder passes, the policeman steps on the accelerator. If the police car's acceleration is 2.00 $\mathrm{~m} / \mathrm{s}^{2}$, how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)?   

  Assume in Problem 50 that the speeder’s speed is not known. If th:o cgm uw*:4zhak wd.1jrt+:se police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was the speedeh+1tjwzm dou :kr:a*wc.:sg4 r’s speed?    km/h

  Two cars approach a street corner at (,lf)a-0* r rfum oaferight angles to each other (Fig. below). Car 1 travels a ,-f)fol0 far*em(ar ut 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 d -thlr7 uh/w7tistance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aimur7thl -7wt /h 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 andosw3pji+6 ( ep 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 dis ip6 wj(e3po+splacement 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.cah7on lkwb (+jnda-:0fm8g;jp c *u sometimes placed to the side of the roadd7jm:(gl8h* k-; u ncfan0.wbj aopc+ for trucks whose brakes might fail. Assuming a constant upward slope of 32$^{\circ}$ , calculate the horizontal and vertical components of the acceleration of a truck that slowed from 120 $\mathrm{~km} / \mathrm{h}$ to rest in 6.0 s . See Fig. below

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

  What is the y component of a vector (inuf)ckjt 3fj .8 the x y plane) whose magnitude is 88.5 and whose3).f 8jctufj k 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 anx5( ajxgi.v/: a(febvgle $\theta=30^{\circ}$ 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 soutp2 *nir xk7e bp7kc)m;ci7z /.btuj- sh 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 p5cg(6gd j 8ftg+ka7 l$\mathrm{~km} / \mathrm{h}$ 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 horizontal s l:j7vu w m4jn,jx,6blpel6x7jmj 4 u b,vjwn,:led is 9.1 $\mathrm{~m} / \mathrm{s} $ as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright - that is, the same way he left the ground. t =    y =   

  Apollo astronauts took a “nine i6xf45ltd ie (aron” to the Moon and hit a golf ball about 180 m! Assuming that the swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only 35 m, estimate the acce l6e(4f xa5idtleration 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 the 7.5d pza6 bkj(z5d,rig1u ;f (;dy$-\mathrm{m}$ -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 platformszs ag,t8+qknxb:f(x .obq/i 5 about 35 m above the water, but they must clear rocky ou.t: 5nq bsbf( x+,kxizq/o8ga tcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. below. What minimum pushoff speed is necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontally. What minii/lxvx2 ,z q-lmum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is “launchq-2 i,zlx/ lxved” 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 co7qj eg2tv1j b6,erm- unstant $215 \mathrm{~km} / \mathrm{h}$ 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 . z-7vij ;o9o1nfmtswt 0xi-) t The boat 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 tripism) 0t xo on79v1;jiwt-tf z- 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 gr6g; ow+ rah;guound level to the top of a cliff which is 195 m away and 155 m ahwug;;gro +6high (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 heigh t- t:49zh8vtgqo(sie t of 2.10 m above the floor. The basket is 2.60 m above the floor. The player likesvsi4 tzq9(get -toh 8: to shoot the ball at a 38.0$^{\circ}$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22 \mathrm{~m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves the end of s4ikco;/wb b6a $5.0-\mathrm{m}$ -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 overjz3el/ r/kk9 lt wxk)6zre:o-pj4 ;g1.zou fi eight cars parked side by side below a horizok/rle ioo)ej zkpfk:txjz r 1gwz4;3u9/- l.6ntal 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 0.94j6qu0m r+05 tdq2ld09l qiug;plf-baog hv(0 m above the ground at an angle of 5vdut 06-umfj(q qld0 h 9 2+gbpq o;ri4lal0g $61^{\circ}$ 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 sp05gp7i ;z9rvgpodjm ng y;j3 .eed of $32 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    $^{\circ}$

  A ball is shot from the top of a building with an initial velocity ofm,y /mc-gurubm ja74 )bzpc*) 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart gun, and being a clever physics student you ,4i )fpyzv08zz8 vvg ndecide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horiz) y z8, p8zvvzgv40finontal range of your gun?