One car travels due east at a9lcr)n t3cnp: nd a second car travels north at Are their velocities eq )rpc3ln n:c9tual? Explain.

Can you give several examples of an objpwol(p w6(hn1+sg 83ttf )knh ect’s motion in which a great distance is traveled but the displacementn 8oh+w gw1h6 k3) t(fp(nstlp is zero?

Can the displacement vector for a particle moving k;1n(znpur,czf4i,uam 2d:m in two dimensions ever be longer than the length of path traveled by the particle over the same time interval? Can it ever be less? Discpzmn n,d (frm4k,czai; :uu 12uss.

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

  Two vectors have length ,4q:jizt ;v 4 urwyot1$ 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))czx4 c:j-um3 pfdv kvtb0eced+46e magnitude add up to give the zero vector? Can three unequal vectors? Under what conditions?0kp)f -emvt4ubjx +63ez c:4)ed ccdv

Can the magnitude of a vector ever (a) be equal to one of its cxix.ag)i 11j8hvjg 7 eomponents, or (b) be less than one of its components?.g 8jji xxh1 av1e)i7g

  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” th0r fblm)kqm-zku :4u(8 b2ijx e riders first hop onto a moving walkway and then onto th r-qzjlbubm2 ux04)im (k8:fke cars themselves. Why is this done?

If you are riding on a train that speedsu2 n+gf2+ ex;x1h irec past another train moving in the same direction on an adjacent track, it appears that the other t e+h x f2eunxgi2+1rc;rain is moving backward. Why?

If you stand motionless under an umbrella in a rainstorm wherm(pt)paf )w*n e the drops fall vertically, you remain relatively dry. However, if you start running, the rain begins to hit p tw )(f)*mpnayour legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at const1bxqi vmn: pm3vk 91emt)/4zrant velocity, throws a ball straight up into the air in mpt):9xv1mbqn/ ie mr1v 4k z3her 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, set off across a 1 2noi:n rtv8kriver 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 nok12v i:r t8na point opposite the starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baseba4 b zq/39uxt-i no0. btc;nukmll player “judges” the flight of a fly ball? Which equation in this Chapter becomq0/onkzit tm4u9.b bn3-c x ;ues part of the player’s intuition?

In archery, should the arrow be aimed directly at the ta9h veyl7jv2fdb +q b5/(rvk1lrget? How should your angle bd r1lvv5v7h+bkefjy l(q2/ 9of aim depend on the distance to the target?

  A projectile is launchedfaovz lv/1y +03 8lifw at 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 the ground with identical initc* cx0z3:r,z bpzt re )az0d)yial speeds, but w:3capd0 *,z rxeb yc0zr))zztith $ \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 thetq o1216vvj xen 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagroxt1jv 612veqam.

  A delivery truck travelx p5r+.vf o8u0 (afhmm: 6ocdts 18 blocks north, 10 blocks east, and 16 blocks south. What is its final :mft+0m.axcf duov 5pho (86 rdisplacement 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 resultak-vu;((vk u.y6ad lj rnt of the following three vector displacements:k. jvdukv(y l(;rua6- (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 vector hbbtudm g,56 , $\overrightarrow{\mathbf{V}}$ 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 +,*fnd tflnx04tuqi8 uo7 . jh $735 \mathrm{~km} / \mathrm{h}$ 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. bel 88q6j udbmao)ow. Their magnitudes are given in arbitrary units. Determine the sum of the three vecto jmo 8bdqu86a)rs. Give the resultant in terms of (a) components, (b) magnitude and angle with the x axis.


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

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



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

  (a) Given the vectoryc( cx0p6 4r5q.wa;a ojz lv(zs $ \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 me .e-mhbxrv 5( 0wjk2fe8 .cwotwps8+h asured on a map to be 4580 m horizontally from the campj 0(x e8+o8w .-bh.pwkrv etw5mfhsc2 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 vecto5fd, fk 7xct +dpj)z9m)0wdqvr in the xy plane that has a magnitude of 70.0 units and a y component of What are the two possibilities for its +fv dkcpdtwm xd,)5q790 zjf )x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a speed iv,4zmak:d z;gm8 .hyof How far from the base of the rz: kiv ;dz,ma.g m84yhock will she land?    m

  A diver running dives out horizontally from the edge of a vertii7zbrs 6.. jzecal cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its base did the b..7e 6jizz rsdiver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water 9-j6mt:c . do.r2b1spsqjslz at a speed of At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)?pj6:1dolc 2mq .ssb9t-j z.rs Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gent)dn eb2*fuk j-ly 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)j b -ekf2d*un 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 laca dwb5l a( r e60dmd2e/.lc4znds 24.0 m from 2a5/ 6ld0c rmecwa(el .dbzd 4the base. What was the ball’s initial speed?   

  A football is kicked at ground level with2zg k* d- n cws85wb 0w68.yy8vroawzr a speed of 18.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at from the roof of(fgcf1f uqq1uq o z*;c .g31nh a building lands 36.0 m from the base (1hgqof.3c cufg uq;z *f11nqof the building. How tall is the building?    m

  An athlete executing a long jump lier ,, )8mz8gop rb9rgeaves 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 hvjn g nx86 *1tbf16hc(cmv1o jump on the Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moon is one-si t8 g6cmv(h c1nnxoj*b 6v1f1hxth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 75,tdfhx :v utr;k9 f15kq07tmu .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 suphxzz2 mr yw,wk 8- ava4mrk8m5w.-l5qplies to flood victims isolated on a patch of land 160 m below. The supplies should be-z m5kww5raylkzv88-hm2 wa m.x ,rq4 dropped how many seconds before the plane is directly overhead?    s

Show that the speed with which a projectile leaves the ground is equal to its speed just before it strikes the ground at the end of its journey, assuming the firing level equals the landing level.

  A projectile is fired with an initial speed of at an angxp vtk5dd 1rh vk9h-ot6o ;0x8le 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 gdy +rcz u0js0cmn-; d0 bwp,h3round level with an initial speed 0cp 3;srydhu+ ,0bzwcn m-jd0of 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 initialrp /x /v(vuh lf6xn*r7 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 t62g(w 3 dv;frvpwovr-he range of a projectile equal its maximum height?wr o;r df6v(-2vgpw 3v    ${\circ}$

Revisit Conceptual Examplr q+o*k.8w yfzswo.p+ e 3-7, and assume that the boy with the slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon isf+r.zy*w o8sp w+oq.k shot.

  A rescue plane wants to drop supplies to isolg wd,htlr9.9 zy w(2fr:f .rikated mountain climbers on a rocky ridge 235 m below. If the plane is traveling ho t9rrfiwg( 2 hl.:z.df wry,k9rizontally 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 aq:6b wflilmu7;d te d+ 15:jcp cruise ship is running toward the bow (front) of the ship at 2.uw:1 dec7bj+:d; t mq6pllfi5 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.kwu hn/ ervf.9;.h 0dc60$ \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 highcc:m: e(7xcaj way 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 2.3 a dm1 ;v/.w4asip6 j)s0j:*yfwbxcvj0$ \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 3ls4i9dx 9 aspother head-on. Each has a speed of and they spot each other when they are initially 11.0 km apart. How much time do the pisasl3 4dxp9i 9lots have to take evasive action?    s

  An airplane is heading due south at a sw sk 3-m*grc9revv5/cpeed 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 thatg((jjs/u : x*itoyk e4 it will fly due south o(t*j/y(ius j:gxk4e?    $^{\circ} $ east of south

  Determine the speed of p c.arxvw 5kr)p960tp the boat with respect to the shore in Example 3–11.   

  A passenger on a boat moving at 1b a.g1z*pouk;u t )ygj*;3g*d sc-pf i.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 dk2.+updi4-rc jgykk +d,o-o2.60 $\mathrm{~m} / \mathrm{s}$ 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 cg48y9d lw dv(byp8 *bstill 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 swimming 0.45 t:gu 5yav 54egmv 39rb$\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 0.45 279 e) ntkvz:w f. ;iodtyhn2,jqa;ww $\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 is4k+v7vz76fj igfvi1zr ipw7 2 620$ \mathrm{~km} / \mathrm{h}$ is supposed to fly in a straight path 35.0$^{\circ}$ north of east. But a steady 95$ \mathrm{~km} / \mathrm{h} $ wind is blowing from the north. In what direction should the plane head?    $^{\circ} $ north of east

  An unmarked police car, traveling a cvab* *k o6*zpyonstant 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 polikx8buf h/5dm.ce car accelerates uniformly as given above, and overtakexb5 ku8. df/hms the speeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street cor, u quh5p:mj:fner at right angles to each other (Fig. below). Car 1 travels at a speed relative to Earmhf :uq5ujp ,:th $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , and car 2 at $v_{2 \mathrm{E}}=55 \mathrm{~km} / \mathrm{h}$ . What is the relative velocity of car 1 as seen by car 2 ?    km/h    $\theta$$^{\circ} $ West of North
What is the velocity of car 2 relative to car 1 ?    km/h    $\theta$ $^{\circ} $ south of east

  William Tell must split the apple atop his son's head from a distance of 27 ms( kg.oxkltvowqo2po)b4 ; v6k:6gd . . When William aims directly at the apple, the arrow isbg; :.kld vg sqtk 6(o2owk.oxp)4 o6v 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 east and 25 m south, and the8:l hecn12)rr;p xq8wrdsf yhlk g, 8.n takes an elecrw8)r8d ;.1f:s8 n y lex2q,hklrhgp vator 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? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

The result is that the displacement is    m , at an angle of    $^{\circ}$ South of East, and    $^{\circ}$ Below the Horizontal.

  On mountainous downhill roads, escape routes are sometimes placed tyw9,w s or/c)fo the side of the road for trucks whose brakes might fail. Assuming a constant upwardwo)fc 9wr/ ,sy 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 (iw:gst j ,*ibs,4cv bv1n the x y plane) whose magnitude is 88.5 and whose swv,:sb c j,bi1 vt*4g 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 angl..5qiu 0n5m8ay4azrv ab lgo9e $\theta=30^{\circ}$ 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 headedyc xl q+m*5ot* due 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 p-8sk;yys0pa ,j 3mlg6 )e mzo) 8gilj$\mathrm{~km} / \mathrm{h}$ 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 jub0id o u.zg wfu8pv,i d40fmd0 frn;7-mping 8.0 m . Assuming his horizontal spev4uigdrip ,.nwmfd uo0 d8;7b- 0ff0 zed 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 sm+8sdu0e7ec e xg0h(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.s8 d+g e(00uexem cs7h (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a hlo5gq/1-;k21oph myp 4ha qv iomer 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 push offi /7u kicdmd)+vn qi- g7yv,a1 horizontally from rock platforms about 35 m above ty,vd1ini viu+ m-gq)/7ac 7dkhe water, but they must clear rocky outcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. below. What minimum pushoff speed is necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis plud 4+kfbd+a6tdp,k 5, hp7 vbwayer aims to hit the ball horizontally. What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is “launched” from a height of uk5pa +b kv46+dwpd df, b,th72.50 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 constant )l 3 zow:appb.$215 \mathrm{~km} / \mathrm{h}$ 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 make a round trip it)*;coo9haz n .yuwfl1f 7u)c4q (jqnn a river whose current travels at speed u . Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving (a) upstream and back downstream, (b) directly across the river (lq*z7 ).u)n oqac4no 9fj;tcfhuyw1and back. We must assume u

  A projectile is launched from ground level to the top of a cliff which isp0qn q963fqrd;.hrvfu2t b1l 195 m away and 155 m high (see pff t6n. 3r 2qq 901bhuqd;lrv
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 above the flooo6j0f, xkj x,ij b ys pe(,w5ksv6-m/vr. The basket is 2.60 m abovmkb6vj 6(o,ewf xj,sy5 0/p,skx-jive the floor. The player 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 theobf-z4h ) em,/ dpl-mupp6anjk j3u-7 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 ca16h l .l zf9ejlq:kcak t*f3c3rcr 8p8r jump over eight cars parked side by side below a h9 :l fqh3leal83cc tkck8fp.z1r*6rj orizontal 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 ba14fv i ihpkms ..+4bamll which leaves the bat 0.90 m above the ground at an angle of a1.mkp fb+s 44ivi.hm $61^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s} $ heading toward centerfield. Ignore air resistance.
(a) How far from home plate would the ball land if not caught?   
(b) The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level.

Find his speed.   

  At t=0 a batter hits a baseball with an initial speed of 1q8uowoi3fz, $32 \mathrm{~m} / \mathrm{s}$ 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 of 1e(wigz,yo 2iuge/0 d-q/ pj9q8$ \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 decide to do a(l7er*m0j io vc.)bg 9jpne:i k:5aua 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 horizokaje0l ( i*)5mipvbgn:ear9 :c7oju. ntal range of your gun?