One car travels due east at and rz: e2ur1y) lja second car travels north at Are their velocities equal? re)lu rj1y: 2zExplain.

Can you give several examples of an object’s motiotjg84sq3j3qs rt,+b p n in which a great distance is traveled but the displacetgqt3 3sjp, b+8rq4j sment is zero?

Can the displacement vector f)eenfl 50qld 0lb,ew7sl4 p n-or a particle moving in two dimensions ever be longer than the length of path traveled by the particle over tnlq4le,ef )lnswped-0 l7 05bhe 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 lengthquzk59vrl3 0b $ 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 uylx ;r :u+ajbc-wx j 61ly2s.4nxnah.nequal magnitude add up to give the zero vector? Can three unequal vectors? Un +xnlwrx6j;y b.2 uyl-j: .hn41asc xader what conditions?

Can the magnitude of a vector yiqr.gx4*/2bb bq2g+nq4rb o ever (a) be equal to one of its components, or (b) be less than one of .q4 brg 2*ob/4b+2yqgqb inxr 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 ridv8xhn- gc.z6p;kd4z mers first hop onto a moving walkway and thxn 8gcpzv;h6 -4 zmdk.en onto the cars themselves. Why is this done?

If you are riding on a train that speedkjdk.5 kb et;/ q5jb6 n-fu6mfs past another train moving in the same direction on an adjacent track, it appearsfbukn5f- jm j k5;qe.6/t6dbk that the other train is moving backward. Why?

If you stand motionless r a2 x)jztfafn47(hh5 under an umbrella in a rainstorm where the drops fall vertically, you remain relatively dry. However, if you start r2rnh7aj) (zfh45tax funning, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an en o qibid5i:b08 by75rrclosed train car, moving at constant velocity, throws a ball straight : r ob8 05yq5diiir7bbup 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 samzbakoxiaza,) 0h ;9 37t-)cc zds mmp1e speed in still water, set off across a river at th)hc- tb 0z;a3)axzazs7ipmo k,19cdme same time. A heads straight across and is pulled downstream somewhat by the current. The B heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baxjcey;b.0d:, hv1xu wxc 5e p8seball player “judges” the flight of a fly ball? Which equation in this Chapter becomes part of thd1;xecc58jxxub .h:vwe p 0y,e player’s intuition?

In archery, should the arrow be aimed directly at the target jxvzp 40 r+*d56fwecf? How should your ang*0xj +5 c6zwfr df4pevle of aim depend on the distance to the target?

  A projectile is launched ssa f+zma h gcan80/ b 1jaa;1h3q*8ifat an angle of $30^{\circ}$ to the horizontal with a speed of $ 30 \mathrm{~m} / \mathrm{s}$. How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch?   

  Two cannonballs, A and B , are fired from thef ,76tcu zwkcc5-cc/k ground with identical initial speeds, 6zct,cc5k 7 fc-/ cuwkbut 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 k /ov :q.dm5ya w;c(aghwiu34k m southwest. What is the displacement of the car from the point of origin (maggk5 q.imw4co/ aav:h(; 3uywdnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 blfp6t3c) ywhq z0n-8+ ec6 jovpocks south. What is its final displacement from the origin? Assume the blocks are equal lez ot 0) 6vc6ef8ypcp+-wjhnq3 ngth.    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 dispm(dg(jyx3 4s (akjmr mlc(5-clacements: (1) j a4xy(cr mmgl3dkj((c 5s-(m$ 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 ve:m86c3b o4;e:cggaa hw:z ktmctor $\overrightarrow{\mathbf{V}}$ 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 traveling kg ly .q,8w 6m; mkiw:if+9uyx$735 \mathrm{~km} / \mathrm{h}$ 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 arbitrary uhqbc; ;f,3rasnits. Determine the sum of the three vectors. Give the resultbqfhsca 3r ,;;ant in terms of (a) components, (b) magnitude and angle with the x axis.


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

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



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

  (a) Given the vector,nbx gjvzqts2qjp5 j+ d691 6ks $ \overrightarrow{\mathbf{A}}$ and $ \overrightarrow{\mathbf{B}}$ shown in Fig. below , determine $\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}$ . (b) Determine $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}$ without using your answer in (a) . Then compare your results and see if they are opposite.


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

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




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

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



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

  The summit of a mountain, 2450 m above base camp, is measured on n,2zu fa*j)j-qbqr/0 zcfq( sa map to be 4580 m horizont q,2fsuajrfcn z bq-*jqz)(0/ally from the camp in a direction $32.5^{\circ}$ west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north, and z axis up. x =    y =    $|\overrightarrow{\mathbf{r}}|$ =   

  You are given a vector in the xy plane that has a magnit natzexaz/d)grt4(7 6ude of 70.0 units and a y component of What are the two possibilities 6 a d)(4e7atztzng/rxfor its x component? x = $\pm$   

  A tiger leaps horizon s*;; +/oa2ecn/y2 v emcolheu wgs1b(tally from a 6.5-m-high rock with a speed of How far from the base of the rock will she land? 2*/vo ; nu alc boyh1s;e(m2+/cesgwe   m

  A diver running dives out horizontally from the edge of a vertica7h 7 9k.4ytojg;p:n gbjleui3 l cliff and 3.0 s later reaches the water below. How high was the cliff, a o;74 npgh7y.eub 3:l9jtjigknd 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 wh6ii+3c ;z 8ukcdwmwjrc1 w93jat angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are w;wmik3w36 rccuicdzj+ 1j89 there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gentlyy )ksgnil72+/d shctvh9yt. ( up to Juliet’s window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the pebbles going when they hi+v79( di sy/s.h2ctnhgtyk) lt her window?    m/s

  A ball is thrown horizontally from the roof of a buildin4r xts ijx3i m/ew 8m62vfx:lzw*(b1d g 45.0 m tall and lands 23v2(rwi1mj*bx /f esmx w l8t6xz:4id4.0 m from the base. What was the ball’s initial speed?   

  A football is kicked at ground level with a speed of 18.0nhvu(l p).srmakfqp v ;(h8bd-w*-x :mk6;c m $\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 horizonta:1,zqdvdk3kxbsrg :(lly at from the roof of a building lands 36.0 m from the base of the building. How tall z: gbdksd1k(3 :qvr,x is the building?    m

  An athlete executing a long jump leiyxj, -q9j7v dc-why-ya8/o faves 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 Moon as comparl,rb(5 oj d3 rylqmv:1ed to the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Mry3qv r(jb: m ll1od,5oon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 75o wafs-i-r9d0.0 m away.
(a) If the bullet leaves the gun at a speed of by how much will it miss the target?  
(b) At what angle should the gun be aimed so as to hit the target?    $^{\circ}$

  The pilot of an airplane traveling wants to drop supplies to flood vicf 0m2 ;rllh.zmtims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhead? 2 lh .zmrfml;0   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 wit j:xty 2 +b1,t:cpfiwxh 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 an i ym2uwb be5h s7gu1s;7nitial speed of at an angle of 37.0º with ygs 717e2;5 wmhuubbs 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 so ;.4scx h0/tibr tolgn+- do9hot with 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 a-e,jt oeg*dk8 ngle will the range of a projectile equal its maximum heighte-*,egkt 8jdo ?    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the slingshot is bxz j,h ,1k1pnx+ 2dhfzelow 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 tree makes the wrong movzhx xf1zpkh2 +n,,1 dje by letting go at the moment the water balloon is shot.

  A rescue plane wants to drop supplies to isolated,ja2serl pge 8-p;ky vlv6d-* mountain climbers on a rocky ridge 235 m below. If the plane is trave avl8 e2gyr *djs,-; ev6pkpl-ling 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 i+8gzk 8t nd.i;j2kvous running toward the bow (front) of the shvjt z.dku+kgn 28i 8;oip 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 ha0f:dnr m*o3w1q5 xk41cw vj 0.60$ \mathrm{~m} / \mathrm{s}$ across his raft (that is, he walks perpendicular to the raft's motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.70$ \mathrm{~m} / \mathrm{s}$ relative to the river bank (Fig. 3-38). What is Huck's velocity (speed and direction) relative to the river bank?Magnitude =    Direction =    $^{\circ}$

  You are driving south on a highway at vk96q 4t.i)khgvy af1 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.s25bjrzz re-k/g 1-z(i/ pe lv30$ \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 a speed of and the*u :e 4wjj7 rhpzv5db76wap z5famd58y spot each other when they are initially 11.0 km apart. How much time do the pilots have to take evadmaf wb8j:wjae57rp5p75*uz4 hv6 dzsive action?    s

  An airplane is heading due southewtj t h78+bb: 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 . fy o nx5 (xb4ystmw8t((no3 d8unq3hin Problem 41 so that it will fly due sout nbo53mx8 ytx38.t((fw yndo4sqhn(u h?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shore in Example 3–11.h c4do:89yfdsp03rjho jz-, n   

  A passenger on a boat moving at 1k djabyvy +4pjhi -r;xhm2u3 m/e/+5j.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 i x6r3yarxd+ /iotjj7r+y +6uwco2:w 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)o(u)f);rg l8eaiojx -ovd) f 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 swimmin3,rcf wv:4tqd:q bzdd. ,qkg+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 * skg 84/wv-rti;q i*w br;jcw93subhswimming 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 su 6ha q(i3lpmkjm 7,u6peed is 620$ \mathrm{~km} / \mathrm{h}$ is supposed to fly in a straight path 35.0$^{\circ}$ north of east. But a steady 95$ \mathrm{~km} / \mathrm{h} $ wind is blowing from the north. In what direction should the plane head?    $^{\circ} $ north of east

  An unmarked police carhseg45jshdv vow4 2r*8qh 0krcu + a+5, 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 the speeder’s speed is not known. If the police car qfks,40sh- h:loql bt 5lu(p5 accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was the speeder’s speed? ho-u q k: q5lsth4f5sp,l0l(b    km/h

  Two cars approach a street corner at right anglesj2k( jh,5u 62gn e(f+l scv,xxnsz,vl to each other (Fig. below). Car nfjv hscgsnx2ke (,, ljl(6 u,2+5zxv1 travels 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-6. zilrcz(;n b:u* 6b,dmub6wuqdvd head from a distance of 27 m . When William aims directly at the apple, the arrow is horizonvdubddlb .u66urqczzb 6w,m;: n(-* i tal. At what angle must he aim it to hit the apple if the arrow travels at a speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25 m south,g6;.x)*e1 dnc tvqdfp 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 relativefn *6 eqp;1)tcdg. xdv 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 roa7 9:duz04 f ovplzxve,ds, escape routes are sometimes placed to the side of the 49pzv z dvux:l,e 07foroad 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 o l5k gznyrsg)l)u((-cf a vector (in the x y plane) whose magnitude is 88k)z5)lu-slcn(g(ry g .5 and whose x component is
75.4? What is the direction of this vector (angle it makes with the x axis)?
$\text { Direction }$=    $^{\circ}$$ \text { relative to } x \text { axis }$

  Raindrops make an angleq3ae.fp cs:ei9a,( nr $\theta=30^{\circ}$ 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 a9wq m +j6uc7ay 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 mtlu937b5mns 3n m:8 )w jwfaj$\mathrm{~km} / \mathrm{h}$ 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 8.0f1uislxnc4xy2(8 x* o m . Assuming his horizontal speedo*2 cysif4ln18 xux(x 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 iron” to the Moon and hit a golf ball al l)ruj:lqu6n9 jk7x6 bout 180 m! Assuming that the swing, launch angle, and so on, were the same as on Earth wher 6qr7n u:6x9kllul)j je 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 the h +o;t bf4-r y:gjsg-) q,ttoy 7.5$-\mathrm{m}$ -high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat?    Assume the ball was hit 1.0 m above the ground and its path initially made a 38$^{\circ}$ angle with the ground.

  The cliff divers of Acapulco push off horipl qee*qsi h/6kl:0 i2d *g7bjzontally 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 froq:kqsbhi76ij ge*pd * l0/l2em 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 horizontallyfh+ 3dz9mblt: . What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the se :fd+m3z lh9btrver if the ball is “launched” from a height of 2.50 m? $\approx$    Where will the ball land if it just clears the net (and will it be “good” in the sense that it lands within 7.0 m of the net)? How long will it be in the air? $\approx$    See Fig. below.

  Spymaster Paul, flying a cons*5w6:dqn2rmghsm f5h tant $215 \mathrm{~km} / \mathrm{h}$ 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 stilkod4hru dpu(w x:f,o3/ *s+mcl water is v . 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 trip of total disto*mxp (udkfoh3/r,4+ cw: sudance 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 cli,8i ulwvs s(qt99 ib-6 ziod2off which is 195 m away and 155 ludzo9i(- si8w69i2,vbos qt 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 au6 9r gf8dt 0n:t6iot vf4qnz9 player's hands at a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The plat 9trnt684i0qffvgzd 96n u o:yer likes to shoot the ball at a 38.0$^{\circ}$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22 \mathrm{~m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves the en 7nc +lzp83aqwiq*v+u d of a $5.0-\mathrm{m}$ -high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine
( a ) her initial velocity, $ \overrightarrow{\mathbf{v}}_{0}$ ,    ${ }^{\circ} \text { above the horizontal }$
(b) the maximum height reached,   
(c) the velocity $ \overrightarrow{\mathbf{v}}_{\mathrm{f}}$ with which she enters the water.    $^{\circ} $ $\text { (below the horizontal) }$

  A stunt driver wants to make his car jump over eight carxo*en *u m63qls parked side by side belol3u*xqo 6*enmw a 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 0a 2.ubphurb c-m- yy3xopd .4,.90 m above the ground at an angle of p- .u pud-2ca ,my.byr4b3oxh $61^{\circ}$ 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 initialzk 4:3 ;tqx,jd 2vx y;sprryi+ 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 th +3p-7lcv k lvl4moj/3fjai)vop-we7 e top 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 dao .jrm.akcrq3wqxr;a) m6 dp76)c7c lrt gun, and being a clever physics student you decide to do a quick calculation to 6m)dc7r lq)pak 37.r;qjw mcaocx6r.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 horizontal range of your gun?