One car travels due east at and a second car d;ew * d3lm7la1 dnkt6travels north at Are their velocities en 167dl ekt*m ;dwdla3qual? Explain.

Can you give several examples of an object’s motionqqq)0wtp09sr : e uom0 in which a great distance is traveled but the drqo:uw0sqpm )0t9e0 qisplacement is zero?

Can the displacement vect(:spb c:xf(4rb t.hspw7h8bgor for a particle moving in two dimensions ever be longer than the length of path fsbc b(p8b7w:4:ht(xspgr. h 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 lengt, (vm,eh6i llph $ 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 vam1:a 3 mehxe0*3lvifector? Can three unequal vectors? Ua0 afe:3x3 i eml1m*vhnder what conditions?

Can the magnitude of a vector ever (a g0zh0hd zxk;:g(6h knwj.27ir jj d,r) be equal to one of its components, or (b) be less than one of its comp:kd ih z hjjx(j0 ;z7krnw.rdh62 gg,0onents?

  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 onz scw::f2zu1 e a moving “car” the riders first hop onto a moving w:: zszw2c1f uealkway and then onto the cars themselves. Why is this done?

If you are riding on a train that speeds past another tral t ,e qvlot7.s03tfzo(8hz) w6rjwh*in moving in the same diq l t*0t.l36z jthow(7f,v sr8 )owzherection on an adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under 1rb oc eye.:, nyzd qw0my:i**an umbrella in a rainstorm where the drops fall vertically, *ny*beic1 qmydz0ero: :., wyyou remain relatively dry. However, if you start running, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, movingdf r77gc qqa0, at constant velocity, throws a ball straight up into the air in her referearf dq0 q,7cg7nce 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 cani8kq l,e 6*vwi d,wo-aottw :4 row at the same speed in still water, set off across a river at the same time. A heads straio,t6dl:wa ot,v8 qwk* iiw 4-eght 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 basrlx( la pph7*(eball player “judges” the flight of a fly ball? Which equation in this Chapter becomes part of the pl*apx l(7r(plh ayer’s intuition?

In archery, should the arrow be aimed directly at the target? How shy. 2 qk-ytf:q+ usdva-ould your angy- :2quskdt-ya. +v qfle of aim depend on the distance to the target?

  A projectile is launched y hwdqgw;(;+lat 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 grou +lyqo3, lf(qynd with identical initial speeds, but wiqlylq, y+ 3o(fth $ \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 u 2 (slfogar rm6r2 1b0ul09xdkm southwest. What is the displacement of the car from the point of origin (magnitude and direm baul1(2u9od rrgxl0 r0 6f2sction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 bloom hxn7; igt;3dj1szr9+3x rx cks south. What is its final displacement from the origin?mtg3dn13ox7jsr i 9xr;xzh +; 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 ib zaw18low2y +2ka*gdisplacements: (1gb+w28io wl21k ayza *) $ 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 vectdtfo)l)dhw en/g.e /9or $\overrightarrow{\mathbf{V}}$ 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-dhjm t4mfy4bw 2/:qy $735 \mathrm{~km} / \mathrm{h}$ 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 gw;g*6:)li:v.dkizvn 3 nlk pin arbitrary units. Determine the sum of the three v.*vwdivg;:z)n l: pkglnk i36 ectors. 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 vectorskll*z(9 z4kor73dw o g $ \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, i 8l mfd-r278d7dswvh 7b*3 orn*vdq sms measured on a map to be 4580 m vd27 d*hrbd7nv3f7l sqdsm-o8w r8*mhorizontally from the camp in a direction $32.5^{\circ}$ west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north, and z axis up. x =    y =    $|\overrightarrow{\mathbf{r}}|$ =   

  You are given a vector in the xy plane that has a magnitude of 70.0 ujzatf7/ll)y s)/ yp/zw) 5pfbnits and a y componebltfzzsfw)/a/p7)p ly)y 5 j/nt 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 How far frori +jycol tioca2e*c37 ; rb*,.r+xwam the base of the rock will she land?7cwo.*3xctra ec+ byiai+2, ;lro*r j    m

  A diver running dives ouhkq,rshlz4pzv7;t w*8 - k(xc tr:z2dt horizontally from the edge of a vertical cliff and 3.0 s later reaches the water bell 2:k;tw z8d-*ks47(zhxp tvrqc hrz,ow. How high was the cliff, and how far from its base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water at a speed of :qyjf7w8e/ 5 ukd8pge At what angle(s) should the nozzle point in order that the water land 2/8 kyu7 5:d8qpe fjwge.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, and heq8narlgwhxn;n-i5h; z 3q8gg:ao6/j wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the e6g8q:w-3rgnnx gq hloznia ;8a/;5jhdge 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 building 4 6y/um/jbw q8l,zpoo :5.0 m tall and lands 24.0 m from the base.oozw/6 / ,j8my pql:bu What was the ball’s initial speed?   

  A football is kicked at ground level q1haus,4 i8v 1ae 57jh nicztv2+ew1pwith 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 jix ub- *fu7fdf. 9sx(cj 9)bpsnu6w 5at from the roof of a building lands 36.0 m from the basei(59)fb9xc s bswu.-u6n jfd *uxjfp7 of the building. How tall is the building?    m

  An athlete executing a long jump leaves thei:(a +wjlhlqce 4*nfhy. 0ev3 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 ton83xixqw ol. * the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moo .8xwnqlx*3i on is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 75.0 m away. k(9y7 cct:62qi+q /) ;x,bqxv tlxgiigs8rr z
(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 i(f9dj a2( qa+d- ja k,izs1xeto drop supplies to flood victims isolated on a patch of land 160 m below. The s+axajs q a( jk,(eiz-19dd2fiupplies 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 initial speed of at an angle of 34. eua/+c hn94scj(xh8q e xr*p15$^{\circ}$ 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 wi4a.ah3j6:grruuriy jw0i7 1na : c)fcth an initial speed of at an angle of 37.0º wi0:urn:yf3ha wug1arjij.ic 4 6cr)7a th the horizontal, as shown in Fig. below.
(a) Determine the time taken by the projectile to hit point P at ground level.   
(b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find   
(c) the horizontal and the vertical components of its velocity,   
(d) the magnitude of the velocity, and   
(e) the angle made by the velocity vector with the horizontal.    $^{\circ}$ below the horizon
(f) Find the maximum height above the cliff top reached by the projectile.   

  A shotputter throws the shot with an initial speed of 15.2de.-pb2x g ch5 $\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 projo7o0 w 0bna*scc9*c geyr7pr+ ectile equal its maximum heightc*7obp r0+ angsc7weor*0y9 c?    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with t twehzf6 ,8 / kq+ak2rrqsz:qx(1nt3bhe slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Sho,: 2 t6ka1 n(8zwrhb ztqk3e+/ rfqsxqw 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 srs;do ry z*-,lupplies to isolated mountain climbers on a rocky ridge 2*l-, r; dyzors35 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 mornol r kvj-fa c4u 3h5)40b4mleking jog on the deck of a cruise ship is running toward the 4-mjkluea )04c r45fkbv3o h lbow (front) of the ship at 2.2 $\mathrm{~m} / \mathrm{s}$ while the ship is moving ahead at 7.5 $\mathrm{~m} / \mathrm{s}$ . What is the velocity of the jogger relative to the water?    m/s
Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?    m/s

  Huck Finn walks at a speed of ykh u k)ja48snw*2(ay 0.60$ \mathrm{~m} / \mathrm{s}$ across his raft (that is, he walks perpendicular to the raft's motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.70$ \mathrm{~m} / \mathrm{s}$ relative to the river bank (Fig. 3-38). What is Huck's velocity (speed and direction) relative to the river bank?Magnitude =    Direction =    $^{\circ}$

  You are driving south on gxdjk dy 4c1w0 kmj4pl2.-ar+ 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 2.321p; dwlxb3k gk /h44obt- nfy0$ \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 ar e64(kux0j rznd they spot each other when they are initially 11.0 km apart0(j ezkrx4ru6 . How much time do the pilots have to take evasive action?    s

  An airplane is heading due south at a speew-1p9k7 h:wq+vr)f-my -cuze ,r vjuu d 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/t9b8 qskw**uu tl kq. pilot aim the plane in Problem 41 so that it will fly due s / *l89qu.ktuts*q wbkouth?    $^{\circ} $ east of south

  Determine the speed of the boat with respedb,tj 0e2v8k cct to the shore in Example 3–11.   

  A passenger on a boat moving at 1 w85b tf);yelf ,i,zjy.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 stills gbbryb5u 0*7 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 w :ouuvhgg4j) aw ;z9v m3(slr6ater 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 swiok ah61g ww1l7mming 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 k )7 dl93sv-z.c al:g 1e4w ugxj)caolof 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?    $^{\circ} $
(b) How long will it take her to reach the other side?   

  An airplane whose air speed ee6e vu5n kr.i9kq /(ekz)f:m 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, tryapt/+m4rcp(3olj 1v 3yiz; h8 buhe-aveling a constant 95$ \mathrm{~km} / \mathrm{h}$ , is passed by a speeder traveling 145$ \mathrm{~km} / \mathrm{h}$ .

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

  Assume in Problem 50 that the speeder’s speed is not known. If the polifxe ryxj/;oyf 1 8d9e6ce car accelerates uniformly as given above, xy;fy jxr6od19 f/ e8eand overtakes the speeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner at rigxn8h)a /zq bbe fj3u.3ht angles to each other (Fig. below). Car 1 traqj ).ub/a3b3fh8xzenvels at a speed relative to Earth $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , and car 2 at $v_{2 \mathrm{E}}=55 \mathrm{~km} / \mathrm{h}$ . What is the relative velocity of car 1 as seen by car 2 ?    km/h    $\theta$$^{\circ} $ West of North
What is the velocity of car 2 relative to car 1 ?    km/h    $\theta$ $^{\circ} $ south of east

  William Tell must split the apple atop his son's headk4a cg1 ()x(m9tah2 ur.s dkxw from a distance of 27 m . When Willtr2a94akkc h1( xm.w s(dgu)xiam aims directly at the apple, the arrow 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 nxw 3ur:7blc9 and 25 m south, and then takes an elevator 10 m down intc7:r3b xnluw9 o 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 -+9ix37oajbjqj h 6hu sometimes placed to the side of the road for trucks whose brakes migjj -97uoxhahj 6b iq3+ht 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 plj6di 1v))n kw ogj-rv zv,a-7tane) whose magnitude is 88.5 and whose x compvvogj,nv )dk61ajt )i-wr-7z onent 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 angle s +(e p2*skexu :(ojqec1b;cci0x- ad$\theta=30^{\circ}$ 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 dueh(:nmw;7vq;x boq 1b r 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 ues sym;+fh-ah-0qhh zrha0j 9:/6lq$\mathrm{~km} / \mathrm{h}$ 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 jumi,3 9 qpf7p*3aorf;a z.tmpdgping 8.0 m . Assuming his horizontal speed is 9.1 f aa;ip podmgft *73rq9z,.p3$\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 tb5gdbmev8 e wpem9 5yv4-77zk he 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, estimatemdz4 e 5bw5ev -79by8vekpm7g 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 -/ i.l. gs/.vwc pxcax 7.5$-\mathrm{m}$ -high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat?    Assume the ball was hit 1.0 m above the ground and its path initially made a 38$^{\circ}$ angle with the ground.

  The cliff divers of Acapulco push off horizontally from rock platforms abcel k0srm+ i m5/qav)t e0j4a+out 35 m above the 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 directs 0j)cle ratam+m 5ei+04 vk/qly 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 0+oijd3 u)bpq1k*uoo ball horizontally. What minimum speed is required for the ball to clear the 0.90-m-high net about 1+oqjukd1ub o 0i)3 p*o5.0 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 consta gj(nptl n,ama+o19xl7 4 ,mfznt $215 \mathrm{~km} / \mathrm{h}$ 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 /uo8.g7x+lr qk bhdh, 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 barb dh,kq/o+x7h.g8lu ck downstream, (b) directly across the river and back. We must assume u

  A projectile is launched from ground level to the top of a cliff whir23uti- 9kjbk ch is 195 m away and 155 m high (9 -2tjk3uk ibrsee
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 atyeb9 vy9) g,u+hc.yvb a height of 2.10 m above the floor. The basket is 2.60 m above the floor.9e, vgy)+chb u v9.byy 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 thx5qk;cb0 an 5te 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 car jump over eight cars parked2c wfc2cavzk.i4 -6nn sck-i : side by side belc.4ci a2c2-k f z6: s-cvinnkwow a horizontal ramp

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

  A batter hits a fly ball which leaves the bav;*. mzkwhm8et 0.90 m above the ground at an anglee8wzkmm; *hv . 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 initial speedvy xb) ibf +gyxdl8()rg xo f1omt167f5x/,ic of $32 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    $^{\circ}$

  A ball is shot from the top of a building with an initial vel0 hf;zz eqeefpqh4k1; )i/:dfocity 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 physics studentz/k cws+ndjttob21 5- 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 db+stn ok-1z/j 2cw5tfor the dart to land back at the barrel. What is the maximum horizontal range of your gun?