One car travels due east at and a second car travels nkrp9-w0, / 3edz vptkjorth at Are their velocities equ3w d9-jkp0ktp/rz ev,al? Explain.

Can you give several examplybc +ltng.m5 5es of an object’s motion in which a great distance is traveled but the displacement is zeroblnc5 gt.y m+5?

Can the displacement vector for a partv /lp:kzc40 ylrnyf.7 icle moving in two dimensions ever be longer than the lenynfyr0:z4v. 7cl lp/kgth of path traveled 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 lengt7y-x ;u( *mcjyew ryn3h $ 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 magni.iimxpq ,)1fv tude add up to give the zero vector? Can three uneq,mqp)f .vii 1xual vectors? Under what conditions?

Can the magnitude of a vector ever (a) be equal to one of its componejrubbw)tr sk-:/f *-to eu3b:nts, or (b) be less than one of irs bk u:fu3-:tow -*bbt ej)/rts 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 riderqqga-kjw 6mbv4o/1( u s first hop onto a moving walkk-vuqqbo g6am/ 14( wjway and then onto the cars themselves. Why is this done?

If you are riding on a train that speeds past another train moving in the sbfhj21 j-z,u ;5olxjj ame direction on an adjacent track, it appears that the other train is movino 5z2j,f jh;j 1xlj-ubg backward. Why?

If you stand motionless under an umbrella in a rainst+nombm f xtmsz+0zo::j6+r:o orm where the drops fall vertically, you remain relatively dry. However, if you start running, the rain begins to hit your legs evem 6mbs+x zno:: t+omzorj0f:+n if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, movi)1r ouiqcbgt0m .g1tx 5u12gl ng at constant velocity, throws a ball m1goq52l uicgx1b)t .t10u rgstraight up into the air in her reference frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row at the same speed in still water, set off across a l3wj;69 0/0kb+srj ha get+r4qzkrgiriver at the same time. A heads straight across and is pulled down 43ki;erlt9jgb s q6hwkar0r0+zgj+/ stream 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 baseball player “judges” the flight of a fly ball? Which kzs zvkotsy- ; 4meh.9o84u1 wequation in this Chapter becomes part of the player’s intuitioy48h w 1k.m z4zvs9e;uot-kson?

In archery, should the arrow be aimed directly at the target? How should i) xr,sal, jm)your angle of aim depend on thlam r)sj,x i,)e distance to the target?

  A projectile is launched at an angle qkbmhi71, n-ccl3jqyx p5 m05 qt6ae( 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 , 1 s;.t*n1bnet ,kkftt a2tw87sgxov-sc8o . iare fired from the ground with identical initial speeds, but wi; ,g.tck27w.ot1t*1tn 8sv8eo nisf -stabk xth $ \theta_{\mathrm{A}} $ larger than $ \theta_{\mathrm{B}} $
(a)Which cannonball reaches a higher elevation? ----待选择----AB 
(b) Which stays longer in the air?  ----待选择----AB 
(c) Which travels farther? If the angle of a is 40 $^{\circ}$ the angle of b is 30$^{\circ}$  ----待选择----AB 

A car is driven 215 km west and then 85 km southwest. What ispnhy;yh9 4 eo1 the displacement of the car from the point of origin (magnitude an oph9 4ne1hyy;d direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 bjo kn;v*-ova8g fk6r /locks south. What is its final*f;arko6/jngvvk 8o- 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 f;mcne*wj(fsvx j o 338ollowing three vector displacements:3wjve n8m*xs3(j of;c (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 vector3jxd5;cdujz ,yj)tcni)7j( r $\overrightarrow{\mathbf{V}}$ 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 travelin-jxl*ri+ z4 f s jx4s2 0vsf2+e(idmtbe3qp.cg $735 \mathrm{~km} / \mathrm{h}$ 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 arbitz6*ukap6 6pu wrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and ang6upw a66*u pzkle 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 mh);oa0x /2 eqh1obln$ \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 measure*:v+vfe:(pku8 rdit gyu,b. wd on a map to be 4580 m horizontally from the camp in a d :gt:r.ywud,u(f+ eik vvb*p8 irection $32.5^{\circ}$ 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 theuk 9)m i/na+1kguy2lh xy plane that has a magnitude of 70.0 units and a y co1k9gklnyi um) 2h +/aumponent of What are the two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a speed of 8 7p.t;e 9o a7p1*vvd/obxoeq6bk xpc How far from the base of the rock wil *bte oxk.abce pvdxp/6 o;7p71ovq8 9l she land?    m

  A diver running dives out horizontally from the edge p 196yp brsd4ubpzcu:05x 4 ccof a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and hodur0496b pc ccpz 4upy51:sbx w 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 aam0t.b 7olvx(7g wl52oq6g vq t a speed of At what angle(s) should the nozz2lo7a 6lgo 5 q(mbgwvqvxt. 07le point in order that the water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, .;u1c, b9/v j it-zhqpwm3jw ,wod*kcand he wants the pebbles to hit the window with only a horizontal component of velocity. He iw9k.p ,c c jwdih/wq o1vjut-;z3,mb*s 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 built+v riq h* qgdb0h1.;fding 45.0 m tall and lands 24.0 m from the base. What wasg bq+1*hqitf v; r0.dh the ball’s initial speed?   

  A football is kicked at ground level with a sw70 b3crgwt*z a ;8tyr+y7mx ipeed 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 7w08u i1*: f9 ya*fjpjvrj2lav rbiq* from the roof of a building lands 36.0 m from the base of rfjilj u0qpybv** jr27f 9v8i 1 :*awathe building. How tall is the building?    m

  An athlete executing a long jump leaves the grounjfpb0s .09yoi d 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 permc(xwp9 u8n2dj /*tywek es.9son can jump on the Moon as compared to the Earth if the takeoff speed and angle are m d9./sxe j*k8(e29uty pnw wcthe same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same l(fica7ga a: l5evel) 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 travelinge-l.t0 jlks ; r a+/)hthja5mw wants to drop supplies to flood victims isolatt rl0/ a+; asl ehh.m)j-jtw5ked on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhead?    s

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

  A projectile is fired with an initialq.tbd7l- 3g km 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 i4exjfbiy /+yj 8ts:z1 nitial speed of at an angle of 37.0º with the horizontal+t/ysbxjjzfy 1ei8 :4 , 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 yfo4bcbqx- 9.mi7 pz/.p :bihan 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 projectiuaah v8c9ql0 3oyle8b3ero- : le equal its maximum height?8hu ecl9- arvy 3l80:qoo3abe    ${\circ}$

Revisit Conceptual Example 3-7, and assume that th 6etjcnyv z 1r mcv- dyb1;10kef.6mi7e boy with the slingshot is below the boyme6kb jyfryv 7 d;c1n1 m v6zi0e1c.t- 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 is shot.

  A rescue plane wants to drop ,pdih4om1z w os)5;i1 w+zc;c2w nutnkls,f/ supplies to isolated mountain climbers on a rocky ridcfk 1pnu5so+42nih/1i ,wdz ls ;c o,mwt)zw;ge 235 m below. If the 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 thcq -x zro;(-7etd(uoy e deck of a cruise ship is running toward the bow (front) of the ship at 2.27(zt e cx yud;-orq-(o $\mathrm{~m} / \mathrm{s}$ 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.i ,n8sfeiv96w60$ \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 8 +/nke3egw4jv ch /ii 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 2.3gd id5xy rkx/x;4+u:dl /8oiy0$ \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 1c)+hl:ydpwq ey1 iwu(j h6,wspot each other whenhqhwi ,(u+ cywe 16)pyl:1djw they are initially 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is headin;yf 27 + rqnbv9a5isbtg due south at a speed of 600$ \mathrm{~km} / \mathrm{h} $. If a wind begins blowing from the southwest at a speed of 100 $\mathrm{~km} / \mathrm{h}$ (average), calculate:
(a) the velocity (magnitude and direction) of the plane relative to the ground, and    $^{\circ} $ east of south
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.   
[Hint: First draw a diagram.]

  In what direction should the pilot aim the plane in Prordfaobfi ( rn.,.6wf +blem 41 so that it will fr 6(o d,f+fw fb.i.rnaly due south?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shore in Example 3–11. bw ej-vtlh*t(;3 tk0u0 4 5cpf/ytaph   

  A passenger on a boat moving at q3t ssh-4d bu; 1.50$ \mathrm{~m} / \mathrm{s}$ on a still lake walks up a flight of stairs at a speed of 0.50 $\mathrm{~m} / \mathrm{s}$ (Fig. below). The stairs are angled at $45^{\circ}$ pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?   

  A motorboat whose speed /ry /ui;z pur1s,.joq in still 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 wate5)tiwdr)mec 0a9y, klr 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 onfhxeb5.(v3r6 xwb p*f swimming 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?   
(b) How long will it take her to reach the other side?   

  A swimmer is capable of swimming 0. hm0zgk v(e1w.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 sgspvr2u4 b i h*z26x.4 e9lqcipeed 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 constantchxna) xx9;8i 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 /,buf(mj *jn inot known. If the police car accelerates uniformly as given above, and overtakefj/imu j*(nb, s the speeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner at right angles to each other (Fig. bf7;a2c : xrgmselow). Car 1 travels at a speed rela7sfg;a2cx mr: tive to Earth $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , and car 2 at $v_{2 \mathrm{E}}=55 \mathrm{~km} / \mathrm{h}$ . What is the relative velocity of car 1 as seen by car 2 ?    km/h    $\theta$$^{\circ} $ West of North
What is the velocity of car 2 relative to car 1 ?    km/h    $\theta$ $^{\circ} $ south of east

  William Tell must split the apple atop his son's head from a distanc7l e-zx gb (t7c2 cr;nda5/wtxe of 27 m . When William aims directly at the apple, the arrow is horizontal. At w d z(7twt;l5n7x-2gx bacc/rehat 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 the1h tfxz;5v26v+4 rv y-dh7h+tacfnw yn takes an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and ho127d+h5f+hah yxyz tvr cvf- vn;4wt6rizontal 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 placeeof)u2a aroa i)yqe),ji., ow-0y/)u :qg jpbd to the side of the road for trucks whos y:grpyae.q uieba)au)oqjw/i -)oo, jf20),e brakes might fail. Assuming a constant upward slope of 32$^{\circ}$ , calculate the horizontal and vertical components of the acceleration of a truck that slowed from 120 $\mathrm{~km} / \mathrm{h}$ to rest in 6.0 s . See Fig. below

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

  What is the y component of a vector (in the x y plane) wrm0iimbf)l48 t9r l ijvm* a-,hose magnitude is 88.5 and whose x cr,ir-imml0 f9iv b8tm) al4j*omponent 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 anglebz8)j 1us i6dj $\theta=30^{\circ}$ 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 , wpjkj *xp:f9s 2k dbz(b5dry.c+yn.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 s.o :wl4 eezj0$\mathrm{~km} / \mathrm{h}$ passes a 1.00$-\mathrm{km} $-long train traveling in the same direction on a track that is parallel to the road. If the speed of the train is 75$ \mathrm{~km} / \mathrm{h} $, how long does it take the car to pass the train, and how far will the car have traveled in this time? What are the results if the car and train are instead traveling in opposite directions?

  An Olympic long jumper is capable of jumping 8.0 m . Assuming hi40emi p( qv pb.f*wop.s horizontal speed is 9.1 w.qmpp ip4obfv e( .*0$\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 Mooc:kskx/j *; wjn and hit a golf ball about 180 m! Assuming that the swing, lauscw xkjk*; /:jnch angle, and so on, were the same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over ( /t1w7uu9*tk4s ug j4jydvpcthe 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 pu 7j7jhnfhk)d p.b (;ursh off horizontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water leveld(;p7 k b huhjfrn)7j. 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 play(w1pz p;kfg. ao /ece:er 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 a e/zpg.:ocf1 w kpe;(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 constant yrg6:i13mq,ju q ubj: typ4 j($215 \mathrm{~km} / \mathrm{h}$ 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 *ujwh/,z/w0mtgw( gjsvq7 (i round trip in a river whose current travels at speejjwzuwv7/i(/ q *0 g, tmhw(gsd 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 and back. We must assume u

  A projectile is launchede2i. l66h.b47 a9;dourjzow )yc9tqkys bfb; from ground level to the top of a cliff which is 195 m away and 155 m high (se9qwb); hao.7i 6y fdbok4tz r6 9.bl2jyucse;e
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 z;, z4s v4pivd2.10 m above the floor. The basket is 2.60 m above tizp,v; s4z dv4he 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 endko z xt+rgy6z,l3pa9rgu 1 mx/1z+wz0 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 cxzyfh xo kj6p 4j43*7make his car jump over eight cars parked side by side below a horkpoxyj cxf*z63 j4 7h4izontal ramp

(a) With what minimum speed must he drive off the horizontal ramp? The vertical height of the ramp is 1.5 m above the cars, and the horizontal distance he must clear is 20 m .    $m/s$
(b) If the ramp is now tilted upward, so that "takeoff angle" is $10^{\circ}$ above the horizontal, what is the new minimum speed?    $m/s$

  A batter hits a fly ball which leaves the bat 0.4h()tk,tzq1o;n o zel k68gpe90 m above the ground at an angle o,h1tek6oeo)(tzl4 q; gn pk8z f $61^{\circ}$ 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 sperps:*yx pa8*aj sdi 1vp7pp1. ed of $32 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    $^{\circ}$

  A ball is shot from the top of h b3c;djman4y 6/ 6*fd rxmd0aa 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 gu3; a+xqrd9dp5r y-nt tn, and being a clever physics 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+3;rxp yn9rtq-at d5dtal range of your gun?