One car travels due east aa) aoo 4neq bafgp46b euv+57 th53d8yt and a second car travels north at Are their velocities equal? Exp65yv + eg5 udqf4ahbo8e473tnp)aba olain.

Can you give several examples of an object’s motion j*rhu5wz6 vi. in which a great distance is traveled butw *v6hi. jzru5 the displacement is zero?

Can the displacement vector for a particle moving in two evm.mg 3sf3d4 dimensions ever be longer than the length of path travel. me4gv3d3sfmed by the particle over the same time interval? Can it ever be less? Discuss.

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

  Two vectors have length2 he-hg di; e):ca2fxx $ 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 akb,dqh ky2b7cabx7 ekxsw2 (9-wi2(vector? Can three unequal vectok 7dxwx2h b-7ky2(a,qwkb92 bce i(as rs? Under what conditions?

Can the magnitude of a vector ever (a) be equal to gzde : -is;. r3zc /smr93whexone of its components, or (b) be less than one of its component: c3ed 3izhxesms. rgr/9 z;-ws?

  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 par/id rz:har2 isk 3n22fks, to get on a moving “car” the riders first hop onto a moving walkway and then onto the cars themselvrhf 23/ ndisrkz:a2 2ies. Why is this done?

If you are riding on a traic 6 be4jc6pu6ln that speeds past another train moving in the same direction on an adjacent track, it appears that the other train is movi4 l cpuj6bc6e6ng backward. Why?

If you stand motionless under an umbrella in a j mb 7evca, iaq3+erj04 ew-.crainstorm where the drops fall vertically, you remain relatively dry. However, if you start running, the rain begins to hit your legs even if they remain under+ a3be c7-.ir4jaj ,eqm evwc0 the umbrella. Why?

  A person sitting in an enclosed train car, moving at constant velow6fi1fu / si,rcity, throws a ball straight up into the air in her refe6u/s 1fri,fiwrence 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 c jf 4:, a,9 uf)kyu3 zlg/oz,qwo*xpvacross a river at the sx ,uap4fwu) 3 coz ,jgqz/9 fk:vly*o,ame 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 base)co1 f.apgz0eyndhhozehh1;n(/ 77v ball player “judges” the flight of a fly ball? Which equation in 0)7(z7 h d/za1n1;penogf.y hohvechthis Chapter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly asr: ;)hq w 6 -e,ds v9v/s9)zhfzsdfqmt the target? How should your angle of a/)-s6)frzd:hqqsedf 9 w,s ;9vmhv szim depend on the distance to the target?

  A projectile is launched at kwwbjwxg4 )94j/3cnj04f )scuos o j -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 identium(k(f*z z -lqcal initial speeds, but withmkz -lu(q(z f* $ \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 the df)b9x-ai2a p0hqogu +xl5)v n 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?59fp lhd vao-xxag+ u q)0i2)b Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 5(dn c v 5w1sghehub2+j06qh iblocks south. What is its f b 201ew hsj5nhv(dquigh+5 c6inal displacement from the origin? Assume the blocks are equal length.    blocks

$\text { Show that the vector labeled "incorrect" in Fig. 3-6c is actually the difference of the two vectors. Is it }\\
\overrightarrow{\mathbf{v}}_{2}-\overrightarrow{\mathbf{v}}_{1} \text {, or } \overrightarrow{\mathbf{v}}_{\mathbf{1}}-\overrightarrow{\mathbf{v}}_{\mathbf{2}} ?$

  $\text { If } V_{x}=6.80 \text { units and } V_{y}=-7.40 \text { units, determine the magnitude and direction of } \overrightarrow{\mathbf{V}} \text {. }$ magnitude    units direction    $^{\circ}$

Graphically determine the resultant of the following three vector displaceysmw2a75 qbb yq(h2n lb:,,pements: (,pqbl : q, 7ens yab5bwh2my2(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 vecm+n(bjv 1vt-y tor $\overrightarrow{\mathbf{V}}$ 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 traveli5 ikgy 3ozy23u( ;brnung $735 \mathrm{~km} / \mathrm{h}$ 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 n)3m:p8t2w6c0ci tsv suowo8units. Determine the sum of the three vectors. Give the resultant in terms of (a) componentsmc8 08u )3c:26vtn wspsiootw, (b) magnitude and angle with the x axis.


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

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



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

  (a) Given the vectors fuoq/xyg 5) 312dvbp u$ \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 a map to be9 ak/20lkjxj n 4580 m horizontally from the camp in a di2 /j0jlan9kxk rection $32.5^{\circ}$ 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 plakfzc/42*- vya kq,psfne that has a magnitude of 70.0 units and a y component of What are the two possibilities for its*f/fvs-, 2qyp k4azc k x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a sc1): vyh6 nkx::i ipb(4ipc bipeed of How far from the n:x hbipc:ibv (ciy461:pik ) base of the rock will she land?    m

  A diver running dives oopks ;pxr9f 31v k.j.h0boz:fut horizontally from the edge of a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its base did thek;jf.b rs19kvh.3oo zxp:fp 0 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 a0q 7fp janstw24)q 1uwhat angle(s) should the nozzle point in order that the water land 2.0 m aq40 )uq fjwp1n2 at7saway (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, and h 2ow q)gf+ef4o m.6zpwe wants the pebbles to hit the window with only a horizontal component of velocity. f+oow2emzpw 6 ).4gfq He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontally from the roof of a build9 aq+fkiiun1 7*zwd+fing 45.0 m tall and lands 24.0 m from the base. What was the ball’s in+iwq+fua7k *1z 9i nfditial speed?   

  A football is kicked at grouny1v1 i q6bn 9dd nuqn3 735blsewj;6cnd level with a speed of 18.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at from the roof 5 di1px/751 gwlufal lof a building lands 36.0 m from the base of the building. How talip1/ u55ax7gw lllfd1l is the building?    m

  An athlete executing a longo: w r +(o+-r)trvnhxo jump leaves 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 compared to theog*a;t; l,ltxo5u*m s Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moon is one-sixth whato;ug 5*o;lamx* l,stt it is on Earth.    times

  A hunter aims directly at a target (on the sam; *z z taxa jsrz4ggj +4,v3lch;1bk1se level) 75.0 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 vi -qp68v;qop1 bi8d b;lmrj1d hctims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhea lpd6vhjd;1;ib -p18r8qoq mb d?    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 angle xy 8.n9kes0 yaof 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 edgem*) t+bkaa/,rkk)rtgti. ,bd f(emrn 3,f x2 n of a cliff 125 m above ground level with an initial speed of at an angle of 37.0º with the horizontal, *g2,) entanmf, )ikbd3rt k a+rrt.b/mx(f,k 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 cz3;m lr0flq2) vyzr0with an initial speed of 15.5 $\mathrm{~m} / \mathrm{s} $ at a $ 34.0^{\circ}$ angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 m above the ground.   

  At what projection angle will the range of a projectile equalyrjbji 5;a zdgw.6*dkam e/ 2()qqw/i its maximum heighty /q5jjq *w2rka z/d;ge amdib i(6.w)?    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with the s6b8h0ibn. a kcbla.r2lingshot is below the boy in the tree (Fig. 3-36), and b..0nca2kli b86habrso 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 is shot.

  A rescue plane wants to drop suppliesdr v osid*f:i9rc5b2 6 to isolated mountain climbers on a rocky ridge 235 m below. If thei 2doc:dvrib 6 fs*59r plane is traveling 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 v- zvj(rlzf()x:b g7 kdeck of a cruise ship is running toward the bow (front) of the ship at j-x 7)lg(:b kzvf zv(r2.2 $\mathrm{~m} / \mathrm{s}$ 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. g0aex,tjeyl2r;b9*jhgcfr u8- 0tj+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 fwm9ey- (o;mrdz*ms/6udn( j on a highway at 25 $\mathrm{~m} / \mathrm{s} $ (approximately 55$ \mathrm{mi} / \mathrm{h} ) $in a snowstorm. When you last stopped, you noticed that the snow was coming down vertically, but it is passing the windows of the moving car at an angle of $30^{\circ} $ to the horizontal. Estimate the speed of the snowflakes relative to the car    and relative to the ground.   

  A boat can travel 2.3204qm(ye+ooi cw) a bi0$ \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 they spot eac0gjo 8x 5yp ykn5uxy8.h other when they are initially 11.0 km apart. How much time do the pilots y8koyu5 .y xgx5j8 0pnhave to take evasive action?    s

  An airplane is heading due south at a speed of 608ov(zpc7d i l8+da2 kt0$ \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 thecmq/ i7*qysg qlqgv(z z;x ,)/ 2uozpj:k9a)x plane in Problem 41 so that it will fly si 2cpyj9) qq gkqlag;( /x m zx)qo*:uz/,vz7due south?    $^{\circ} $ east of south

  Determine the speed of the boat with respect bj6q:lare(nn(4 phey hdogq:v7 (.*q to the shore in Example 3–11.   

  A passenger on a boat moving at o-1zbh)b tt8 o1.50$ \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 2.60 x(elid98a 69y5) uxye grfq3r$\mathrm{~m} / \mathrm{s}$ must aim upstream at an angle of 28.5$^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current?   
(b) What is the resultant speed of the boat with respect to the shore?   

  A boat, whose speed in still water is 1.70 )q46nnwimwg fr;io/ 5 /2kaft$\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 yudroqy6+1s; 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 swimm/3 :gyrupa9 lsu4+ asking 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 speedu a5s*sp 0fs kod3y.mcmzrxp/af5 7/0 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 car, traveling a constant 95m r./txc osqy,4 .i,au$ \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 speederai -9k7 h:hcwy’s speed is not known. If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was the spei:yhaw khc7 -9eder’s speed?    km/h

  Two cars approach a strezsteo(y ,m m 5clsk+ .5wr2z+oet corner at right angles to each other (Fig. below). Car 1 travels at a speed relative to Earth k5m ( mcsw5oyr,.lze+t o 2sz+ $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , 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 m . e to9)nt.ju5uWhen William aims directly at the apple, the art 9tun )5e.juorow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25 m south, and then take*x*1kfer 9rggtsq e+t dz:lpye7l/( 0s an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with thg/q l 9e*(7x1e+z*y:sfr dtk t pel0rge 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, 9b6l5 duc;vs)ynt v3v (cf x/9 w5dzwoescape routes are sometimes placed to the side of the road for trucks whose brakes might fail. Assumindf6c v/5 ;lvwowytnz(v b9cu 5sd)3x9 g 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 jfljz1p*kv g:7,* qiw (in the x y plane) whose magnitude is 88.5 and whose x component is vjq*ikwpf:z*lg 7 j,1
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 anghyu xf.yj :*.zjin5q+ le $\theta=30^{\circ}$ with the vertical when viewed through a moving train window (Fig. below). If the speed of the train is $20 \; m/s$ (a) what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically?    $m/s$
(b) what is the speed of the raindrops relative to the train?    $m/s$

  A light plane is headed due sjoba5u/gds u2y. 9: rwouth 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 , td hgx3::ng -)aypielk8:i()zosb0x9x htb $\mathrm{~km} / \mathrm{h}$ 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 imyh/kkyb hnl/a nd83rkcy +l 84y v1:;s capable of jumping 8.0 m . Assuming his horizontal speed is 9.18bcd y+4kyn/h/nkv alm;18 ylrk h y3: $\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 ir m30qc zbx4hxbxw( e;:on” to the Moon and hit a golf ball about 180 m! Assuming that the swing, launch angle, and so on, wzc m x4w(x e3;:h0xqbbere the same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over the 7svax .0m p. pv xc+wi,hy4)pdoj3wub23l.wh,.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 horizo vhwapo9 y7v(bhy.0gn;3pki - 65khry ntally from rock platforms about 35 m above the water, but they must clear;0v 3 a9gh iyr67nohwh v- .bp(kkpyy5 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 player aims to hit the b /4k qjfnk- x*d ;q,:he(trplphp m2x(all horizontally. What minimum speed :em4 h/xt2 kfjxd (h;*nqpr,lpqp-(kis 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 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 coebcr( b pi:;j9nstant $215 \mathrm{~km} / \mathrm{h}$ 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 gxa/yxd.. b9+ p42txz4wl nzyuv-bi5water 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 distance D if the boat makes the round trip by moving (a) upstream and back downstream, xaiy.ugb5 / 4ty+.9plxnx-b d4 wv2 zz(b) directly across the river and back. We must assume u

  A projectile is launched from ground level to the top of h)m n e3.askk-a cliff which is 195 m away and 155 m high (skkn.h-3em a s)ee
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 h;drzdzu.v r (q(lq2x 3ands at a height of 2.10 m above the floor. The bavrrq zqx.dz(23u;l (dsket is 2.60 m above 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 the en ld;dc7*0-x ev0xdosvq6pxl 0 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 cars parked side bguxr gtq9l3/g /.b 1*:umeh54yx fpaqy side below a hor5e/qg*3qtry xp/9fmu:.1g4 xg h abl uizontal 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 th u(3n*em omnt/;yyo; ke bat 0.90 m above the ground at an angle no myk3u tmn(oe;*y;/ of $61^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s} $ heading toward centerfield. Ignore air resistance.
(a) How far from home plate would the ball land if not caught?   
(b) The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level.

Find his speed.   

  At t=0 a batter hits a baseball with an ,,-b nxwnrt ec:ze:vu6( ;hcsinitial speed of $32 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    $^{\circ}$

  A ball is shot from the top r f15 fenf ,1syirz)b7w9 8mimh 1p,ypof a building with an initial velocity of 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart gun, and being a clever phy2q -u)z4zbzby2x -xob sics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizon)xyo2u42zxz - zb b-qbtal range of your gun?