One car travels due east at and a secon7-*0i0eeu kuf5sx nsx d car travels north at Are their velocities eqn*es7-e 0i x f0kuxsu5ual? Explain.

Can you give several examples of an object’s motion in which a great distance rdfpg:ry g;z 8bt034ihf;z q(is traveled but the 3grd;r(8i f; q0ybfz:t4 pzhgdisplacement is zero?

Can the displacement vector for a particle moving)ak/)ch-r)o gc2 psxj in two dimensions ever be longer than the length of pahos2-) /) p)cgarcjx kth 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 length s088ryi( cirz)w gdr( $ 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 gw+*v;u78y1tfka j xx up to give the zero vector? Can three unequaluva8+x1* 7ywk;jftgx vectors? Under what conditions?

Can the magnitude of a8or dd-w*ahai6 2uu x8 vector ever (a) be equal to one of its components, or (b) be le6 ad88i2x-hrauuw*d oss than one of its components?

  Can a particle with constant speed be accelerating? ----待选择----YesNo  What if it has constant velocity? ----待选择----YesNo 

At some amusement parks, ts )yoncv e/,4jo get on a moving “car” the riders first hop onto a moving walkway and then onto the ca n 4cv)/ysoej,rs themselves. Why is this done?

If you are riding on a train that speeds past another train moving in thq k 5qe rw)ut(d(n/3gee same direction on wqrd uen5q/(t( ekg) 3an adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under an umbrells .j)hqn *1,potanh r8q)cpq2f(,.m)mqf smr a in a rainstorm where the drops fall vertically, you remain relatively dry. However, if qcsomqfqrn,jh .hq2n)p) )*f r(,sma.1pmt 8you 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, moving at constant velocity, thr6. yh2rmy iik/ows a ball straight up int2 /ykm.i6rhyi o 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 of2 2(p oxvcpya7f across a river at the same time. A heads st xp7vp2o c2y(araight 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 baseball player “judges” the flight of a fly 8 xjvbbs:7nxx 8 hz7s;: y*jcgball? Which equation in this Chazxnsb7y8sx:xj7gb:8 ;hv *j c pter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the target? How should your ani dqr/7r r-5vegle of aim depend on the disedi rr7v/r q-5tance to the target?

  A projectile is launched at an anglea9jnnda1;nrsr g6 u n5a9p-( f 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 fi y6xez 2wsdp) a4tlp.8red from the ground with identical initial speedsawd.p4tpx6l y)2s8ez , but with $ \theta_{\mathrm{A}} $ larger than $ \theta_{\mathrm{B}} $
(a)Which cannonball reaches a higher elevation? ----待选择----AB 
(b) Which stays longer in the air?  ----待选择----AB 
(c) Which travels farther? If the angle of a is 40 $^{\circ}$ the angle of b is 30$^{\circ}$  ----待选择----AB 

A car is driven 215 km west and then 85 km southwest. What is the dizr/-l e5m,z btsplacement of the car fror t5- mlbezz,/m the point of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 1f)t* b( xm2jya6 blocks south. Wmajxtfb*y) 2( hat is its final 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 tli)lptkb8yy .o5gje--r4d 0h3+ca w jhree vector displacements: (1) k0.t8db aljpghloc-wy-43yj5ri) +e $ 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 vecto,c n1wvp,n7;duv n gz-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 traved,h4 sib+ 8qlb9c- dzpling $735 \mathrm{~km} / \mathrm{h}$ 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. jhif1,jk -7ocfx(f2fj3 ij) qTheir magnitudes are given in arbitrary units. Determine the sum of the three vectors. Gioj,7cjk fj31xiffj- f2 )q(hive 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 vectors wlk5x0cnn)bv yu j.(ffkw.70 $ \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, ismwk tr,fpd 6knu319y( ua0h,e measured on a map to be 4580 m horizontally from the camp in a d(ud k wpf0,unra e,y 36k1htm9irection $32.5^{\circ}$ 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 units wn .d:30a p2 :xta5z9cafumdqgl -uy 9and a y component of What are the two possibilities fa9ng2p:0xlw m.9d a ad u5yqft u-:zc3or its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-tjcy5rmka+g + 4 ,wak;mvg o-5m-high rock with a speed of How far from the b4ay++ ,ctv r ggmmkwko ja5;-5ase of the rock will she land?    m

  A diver running dives out horizontally from the x p:yi)etzs 8g3g 44h:,ljyjjedge of a vertical cliff and 3.0 s later reaches 4:t, sg) xj8eih3y4jpjy: glzthe water below. 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 shil3a mou: h,f45.zh uqwk7)a doots water at a speed of At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. bez,)hauuk5 lha: md.w4qf 37iolow)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, :k y3wa a;xmu1kg 4w6g1nndoas r33t:and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garde 13xrwnak3wm41 k6aaouty s:g 3d:g; nn 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,r6: l(a53ncxga ieeegkqa,x/7 xi(l from the roof of a building 45.0 m tall and lands 24.0 m from the base. What was the ball’s initial speed?qxi,(x 7aagel e(6l3i5:g/ren, a c kx   

  A football is kicked at ground level with a speed of 18baaxr gut/b;. rf45 .g.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at from the roof of af3vr9* zvl eb+ building lands 36.0 m from the bas+vb3 revz 9lf*e of the building. How tall is the building?    m

  An athlete executing a long jump leaves-ea fs;m0d e0r 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 comparqqssj5zo+ (c;, 6 w ;xbtbua3ied to the Earth if the takeoff speed and angle are the same. The acceleration due to g +j;btq3aiz 5c6qbsow u(s ,;xravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 75.0 kum7pn +jzmcos4hp-dhd )d 0:o,sjq.f0i5*om 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 wrw9jn l;lcra6 (u+a2d q:plt(ants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhead?uaa lcqw(pjlt(29ldnr;+6:r    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 i)eafe ty;::;yna *d wknitial 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 abovnar(x ik6f4b w ; l8-/p5tm 4c9esoohse ground level with an initial spe waf(xsoe5- lhbspti rk69;o/ 48cm4 ned of at an angle of 37.0º with the horizontal, as shown in Fig. below.
(a) Determine the time taken by the projectile to hit point P at ground level.   
(b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find   
(c) the horizontal and the vertical components of its velocity,   
(d) the magnitude of the velocity, and   
(e) the angle made by the velocity vector with the horizontal.    $^{\circ}$ below the horizon
(f) Find the maximum height above the cliff top reached by the projectile.   

  A shotputter throws the shot wit*n*jp; um 4fgndkr c1(h 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 a4 -c4ezeuw8hlngle will the range of a projectile equal its maximum height? lc4 we4ezhu-8   ${\circ}$

Revisit Conceptual Example 3-7 +qdj , yn)zmw6e,i/yu, and assume that the boy with the slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree.d/yj n)+muy,,zq wi6e 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 supplies to isolated mountain climbers on a qcc27ck (l,lcrocky ridge 235 m below. If the plane is traveling horizontally w7k(cl,cc 2 qclith a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

(a) how far in advance of the recipients (horizontal distance) must the goods be dropped (Fig. a)?    m
(b) Suppose, instead, that the plane releases the supplies a horizontal distance of 425 m in advance of the mountain climbers. What vertical velocity (up or down)  ----待选择----updown  should the supplies be given so that they arrive precisely at the climbers' position (Fig. b)?    m/s (fill in magnitude here)
(c) With what speed do the supplies land in the latter case?    m/s

  A person going for a morning jog on the deck of a cruise ship is running ta)1,ut wim h ,yiz3a+doward the bow (1 t)amiidayw z,3,hu+ 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 (fzvj /t6r 1,kjq4so *rhez4gspeed of 0.60$ \mathrm{~m} / \mathrm{s}$ across his raft (that is, he walks perpendicular to the raft's motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.70$ \mathrm{~m} / \mathrm{s}$ relative to the river bank (Fig. 3-38). What is Huck's velocity (speed and direction) relative to the river bank?Magnitude =    Direction =    $^{\circ}$

  You are driving south on a hiwm6a m.o:s4* nemrt y:ghway 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 2pm1cd3c a jyw. b7b( amse9rs725br v5.30$ \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/po m*jb32a/jssq i t0 speed of and they spot each other when they are initially 11.0 km apart. How much time do the pilots have to take evasive action?mjqab os2t0 *s/j3/ip    s

  An airplane is heading due south at a speed of 600r+z ;oz8y/nyiz/me2p u p5 (fsobm+j7 $ \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+t83 lhbwj3vu the pilot aim the plane in Problem 41 so that it will fly dubtj+ l38h wvu3e south?    $^{\circ} $ east of south

  Determine the speed of the boat w.an p :ny ,(4r;fd5vtw7gerbtith respect to the shore in Example 3–11.   

  A passenger on a boat moving at ;b7ko03e z10m vt9h jqypa ,rr 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 b zhy0(/ b-,jk gcp-dw+ yq-xpin 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 water is 1.70 l.gpyoaxij4+g9 c8(ywri g0/ $\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 swimmiyp c dxtwfz2e31*x023 jo7a odng 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 swdu m3/ viu p-tjm ) uo97hzmqoml5-(y)imming 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 ic8pxf )9cyp; es 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-30jwsh/m f*t9lnqc b, traveling a constant 95$ \mathrm{~km} / \mathrm{h}$ , is passed by a speeder traveling 145$ \mathrm{~km} / \mathrm{h}$ .

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

  Assume in Problem 50 that the speeder’s speed is not known. If the police ca9i1 7l ,nkte*tn0xu jdr accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was the en,juit1t ldxn70*9kspeeder’s speed?    km/h

  Two cars approach a street corner at right angles to each other (Fig. below)kq40 cy+2b v8-sall xp. Car 1 +p0 c bklsv2y8-x 4qaltravels 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 head f*n0j8g- f )pr/abm-a4z mdg irrom a distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle8 rp-a/*grn f4zi mdga0-j)bm 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.wyilr0vu chax5 e*.ru4d /g4 and 25 m south, and then takes an elevator 10 m down into the basement o.rxwiu * l5hc/ a4vr 0ed.u4ygf 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 som6/gp9 iptyd4z n ot5e6etimes placed to the side of the road for trucks whose brakes might fail. Assuming a consto45tpidy6ng6 pz 9/et ant 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 ve2ep /b0iu sbkdmdrni8 d65q-u0oz5v 4ctor (in the x y plane) whose magnitude is 88.5 and whose x ur- kndzm sov5 udb05ibi/804peqd26 component is
75.4? What is the direction of this vector (angle it makes with the x axis)?
$\text { Direction }$=    $^{\circ}$$ \text { relative to } x \text { axis }$

  Raindrops make an angle lx5wyds og07uv*f :)n $\theta=30^{\circ}$ 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 uuz d6ysp iv:n96* )lkdue 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 6c8vd5qofviva+6 .i:k1 mb j f$\mathrm{~km} / \mathrm{h}$ 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 jumpil-,-+s1pqrefzad o j i .xwd;7ng 8.0 m . Assuming his horizontal speedir f ;.zew,os+- xql-da1dp7j is 9.1 $\mathrm{~m} / \mathrm{s} $ as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright - that is, the same way he left the ground. t =    y =   

  Apollo astronauts took a “nine iph)vf xggt ),/np.rd;ron” to the Moon and hit a golf ball about 180 m! Assuming that the swing, launch angle, and so on, were the same as on Earth whptp)n;g d,f xv gr)h./ere 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 1.; uv7 x6xosw eim;cz7.5$-\mathrm{m}$ -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 abox00rf f-:fm s ws0.h/xqyj-asut 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 directly under their launch point. See Fig. below. What minimum pushoff speed is necessary to clear the roc:0h.smfj asf0s /-q y-wx 0fxrks?    How long are they in the air?   

  At serve, a tennis player c: m n/.l 4uy-iwj+asraims to hit the ball horizontally. What minimum speed is requ+/njyilsw.a-m :u cr4ired 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 d0 uynkg nl 5(mmwb5-y7:(cw ba constant $215 \mathrm{~km} / \mathrm{h}$ 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 sn/kds532nu6eixx7y8z gfy,r uq1 x o9till water is v . The boat is to make a round trip in a river whose current travels at speed u . Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving (a) upson56 yxrui9 x 1 2gxfn,/k87zyuesq3dtream and back downstream, (b) directly across the river and back. We must assume u

  A projectile is launched from ground level to the top of a cliw+c (x5s e5 :o3tdedihff which is 195 m away and 155 m high (see de dst3 e:i5+cxwh (o5
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 heimbm0ha(f j(k dp)f 5mz0n*o ;nght of 2.10 m above the floor. The basket is 2.60 m above the floor. The player likes to shoot the ball at a 3 p0admof mbfjnz0(knm5;(h*)8.0$^{\circ}$ 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 end of agxp*m f8k6y -p $5.0-\mathrm{m}$ -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 carllj e5tly 9 )4.fbqda,s parked side by side below a horiz,jl.9llfqytae d 5)4b ontal 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 0.90 m above the ground at an arxub5o bt f19 2v;yjz+ngle ofj t5 bubzr9v;+yo1 2xf $61^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s} $ heading toward centerfield. Ignore air resistance.
(a) How far from home plate would the ball land if not caught?   
(b) The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level.

Find his speed.   

  At t=0 a batter hits a baseball with an initial speed of j7n ) ovbj*6nzao 31qrgqwi cr2;k+w; $32 \mathrm{~m} / \mathrm{s}$ 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 initial3zy)pz6vls 3 ysf 2h1np9l; pl 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 physics studen,ekfvb f ,wwxo9 3j63st 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 horizontal range 3k,,svbe f6w jxw9fo 3of your gun?