One car travels due east at and a second car travels north at Are thexdeha *q+67d)fh vgd9x l z/nw ,vw2b+ir velocities equal? ,dd+ v 7*+wwhbgx2)vdz l6hxfn/9 a qeExplain.

Can you give several examples of an object’s motion in wh/cxwh35 d2p)ewx4l xa ich a great distance is traveled but the displacement iwe x3)xxc l52d/hwap4 s zero?

Can the displacement vector for a particle movis+fh.sv nl8m*c*jm) xng in two dimensions ever be longeljx)s*fm8 vs . c+hmn*r than the length 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 length c93)djgtp vsa()ysc /$ 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 tol; y(4 8tomw *u6ul 45znxygcz give the zero vector? Can three unequal;u 5u n6cylzowgy44z(xmt8l * vectors? Under what conditions?

Can the magnitude of a vector ever (a) be equal tomqa oi, l.jat jrz8p1j/ d.y24 one of its components, or (b) be less than one z a/,ad 48m2.ji.pj1 yo qljrtof 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, to get on a m e688l bv;tig:t-kwwk6ej / jeoving “car” the riders first hop onto a moving walkway 6 g8 jtije6wv;ek w/bk:el 8t-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 same d j l6pndu*q(keuv-6p8irection on a*pdq u kelj8n66(u -vpn adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under an umbrella in a rainstorm where the drops fallcj+f vk f bn.-9at+kb, vertically, you remain relatively dry. However, if you start running, the rain begins to 9,c-. +tjb fafk n+bkvhit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at constan qzni0n/, yhdm;8byu 1t velocity, throws a ball straight up into the air 0ndyu z/i; mq ,y1hn8bin 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 sab aw6m1)p9 g7gcli8d *zo hfl6me speed in still water, set off across a river at the same time. A heads straight across and is pulled dowlbdh 6w*9)1 m8 7g gfp6lzcaoinstream 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 t(.j8sj3x fj. qh1 rgrq07ptlfly ball? Which equation if (qxl7pj rj s3q0h8 tjg..tr1n this Chapter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the target? How should vf0j sd0i +sjd d)7.ejyour angld .d7s)jvji0ef s jd+0e of aim depend on the distance to the target?

  A projectile is launch4gt8uta ld vjga*a+o ee;q5, 5ed at an angle of $30^{\circ}$ to the horizontal with a speed of $ 30 \mathrm{~m} / \mathrm{s}$. How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch?   

  Two cannonballs, A and B , are fired from))csw7k a)sz s6e9v g0mo yt8+qqd*zm the ground with identical initial speeds, but witqy6* o8)w+dtks ) zqs7vagmcezs)m90h $ \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 wxj2p0-bf w9oeoj j x,h. x5m7vest and then 85 km southwest. What is the displacement of the car from the point of origin (magnmho2,xp bfe7jx.wj90-x j o5 vitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks so4mcx+73.pe ax*lb u kyuth. What is its final disp x*u mly3+keb.x c7ap4lacement from the origin? Assume the blocks are equal length.    blocks

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

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

Graphically determine the resultant of the following three vector f4. q 2igzbu3/ *sxnrbci r*3jdisplacements: (34z rnb3q*s 2r.jxgc*bui /f i1) $ 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 vec xsljrvw:kw,u b 8qj)/7v9p 4rtor $\overrightarrow{\mathbf{V}}$ 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 traveyk69do /tudz0cm-dsuohi hf81c6+ : pling $735 \mathrm{~km} / \mathrm{h}$ 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 magsu2y/3 su ri.rfted 3e,+2drbnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultane+3,2yfrui3d2dr/.tbs r s u et 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*6nku3y /q y3bthpf :r $ \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 mountv)x 9b7.y pgsqain, 2450 m above base camp, is measured on a map to be 4580 m horizontally fr s.vp7xg) 9yqbom 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 hblqmzi ;6 cnp0/m7339l*scf f vc7yxyas a magnitude of 70.0 units and a y component of What are the two possibilities for itsm3sc0 c/fy9b v in776lpqzxm yc l3*;f x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with 9:8cfc+x/uvpn ,hdj plpxz11 :b 9yyya speed of How far from the base of the rock will she l :j+c9 :dz1v c ,yp19xyhynplpx8ub/f and?    m

  A diver running dives out hovtt 3qw0 us*x+q20u b9y xk5wxrizontally from the edge of a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far f2xxt +90syutw 5wv bkxuqq03*rom its base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water ab 4t8,u(ldof rfv- vz7t a speed of At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there two different angles? -7utvfzfodl(4bv,8r Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, and he wants the pebblebp5o(vt 0 y8l r0l7+xsa4 scmos to hit the window with only a horizontal component of velocity. He is standingval o+t7 0yc5x0s4r8( mopslb 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 building 45.0 m tall and landi) h zl 1mc:aek7fhsxb1-d3 ;ms 24.0 m from the base. What was the ball’s i-e x if31ackbhzd;7:smm hl 1)nitial speed?   

  A football is kicked at ground level with a speed of o0tme 8 cvh6t/ 18.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at from the roof of a buildi:o; wxg/sj,n;i(sdrz ng lands 36.0 m from the baosnz:s(j;/ xgr ,;id wse of the building. How tall is the building?    m

  An athlete executing a long jump leaves the gr w)x raer*f(b/ound 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 ca *+t)mzuea7y *o-rt2y4mdopmn jump on the Moon as compared to the Earth if the takeofr ) zt4-aoo+*d y7mtmmepu2* yf speed and angle are the same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a0xuhcm c; afvm4ja,.: target (on the same level) 75.0 m away.
(a) If the bullet leaves the gun at a speed of by how much will it miss the target?  
(b) At what angle should the gun be aimed so as to hit the target?    $^{\circ}$

  The pilot of an airplane traveling wants to drop supplies to fux 8 f8pxue2 3iq.6ie+n.vepklood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is dirkne.iq8px2 p v6 8ieux3f+. ueectly 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 a hp01q0 ahek4ungle 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 c y: wbuym10:s/3ivuv9 l+nmc initial speed of at an angle of 37.0º wit9:iu+/mn ybwv vulc:c 1m3y0sh 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 anz;qv)xxd 4z,e im6mj5 7reiu0 initial speed of 15.5 $\mathrm{~m} / \mathrm{s} $ at a $ 34.0^{\circ}$ angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 m above the ground.   

  At what projection angle will the range of a projectile equal its maaeoe, pbf530h ximum height? h503 epfoba,e   ${\circ}$

Revisit Conceptual Example 3-7, and assume;-nhd l q/v-,a6ox guz that the boy with the slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by,-nq a /-zov ul6dhgx; letting go at the moment the water balloon is shot.

  A rescue plane wants 6 gujb.oh-nwqq tw-n/:be0mhi ww+6) to drop supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is trave/ujn)n-oi 6-ww g: bw.0whme6b+ qhqt ling horizontally with a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

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

  A person going for a morning jog on the deck of a cruise ship is running towg7 +yr*9bsxpglu 3w/paj 9yi ,ard the bo u9wys,a9yr/*gb3xgjp i + p7lw (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 tx*plt+ 8 9gdospeed 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 hig 2fbt) sxyz5an- (29 .aj/kn)trfdjybhway 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 2.3r me t6acjfz *cnq9,i0iu f.-,0$ \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 6ky7+r sp1knpo za42- *j dnxkthey spot each other when they are initially 11.0 km apart. How much time do the pi1z-ax rpk4ns pdk 7y2onkj 6*+lots have to take evasive action?    s

  An airplane is heading due south at a speed ofliq, kemh-;zxf7z 0-r 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 z4wj*b 7nmvip;sw3b7pilot aim the plane in Problem 41 so that it will fly 7zn;jv4*3i ps7 mbwwbdue south?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the shore k d,4hd4/8w 8pmaxhjmaj06 a ein Example 3–11.   

  A passenger on a boat moving at 6xrm4 (s,10uiwk dtg:g k)vxp 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 in still wxspdohic s*0ru2, uy5)a3qh;.yg 9 ccater 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.pvgu,pw7n1 r;cb6p ,u70 $\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 oygtc;)3 ileqycwlj+(* zut64f 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 swimmi i uf3zd4kj);dng 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 aizne7k16+; *o me9bnb0m swgbgr speed 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 cowci2 j-2zqfh.t5kev d6)k m (anstant 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 know;xi wji2 (zc qr:8ox0kwlt1v 0n. If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was8tj0i wkl0crqow2z(1i vxx: ; the speeder’s speed?    km/h

  Two cars approach a street corner at right angles to eacibyt9+h1 dw *n*np2yhym4 -zwh other (Fig. below). Car 1 travels at a speed y-y*n*p 21z9+idt4 ym whw hnbrelative 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 ra :1+9l( ztdntqjr: cz;lia6cpg yrss7s09( head from a distance of 27 m . When William aims directly at the apple, the arrow is hops6q g(d9sc+zcrlst t;a1layj7 (z0 :rn 9 :ririzontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25 i)/dli5oawb . m south, and then takes an e/ ad)i5io.bwl levator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

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

  On mountainous downhill ro4+ cvi n7jd2vdy 5(*y1v urbbpads, escape routes are sometimes placed to the side of the road for vpvcv 5ny(d+b*j42diuy1b 7 r trucks whose 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 compone9ed :vu0njq 3 9,apv c7hx7z+ :baghdent of a vector (in the x y plane) whose magnitude is 88.5 and whose x 90jddhcvvap 93xnq: ,:eb z e7h7u+ga 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 anip)kbuy3ymv3 k* igo,s:/ew- gle $\theta=30^{\circ}$ 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 with a speed of 15qxduhsrxm/zr9k1 c +9p /l5:g5$ \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 sb 2- o )sbq)3g: oj(whkxynm6$\mathrm{~km} / \mathrm{h}$ 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 6 28u vfktu/phcapable of jumping 8.0 m . Assuming his horizontal speed uv6 8u /kp2thfis 9.1 $\mathrm{~m} / \mathrm{s} $ as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright - that is, the same way he left the ground. t =    y =   

  Apollo astronauts took a “nine iron” to the Moon and hit a gop0w9-zlka 70 ala0dxq 3x2ot jlf ball about 180 m! Assuming that the swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air rkqz9xdla 0pjxlt a o-072 03waesistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a :y5:9amf7h+ ,u:wipu,fl oxim r8 rwqhomer over the 7.5$-\mathrm{m}$ -high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat?    Assume the ball was hit 1.0 m above the ground and its path initially made a 38$^{\circ}$ angle with the ground.

  The cliff divers of Acapulco push off horizontally from rock platform q 0k(dwu+ua)js5h1iu+x; mlss about 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+iuu 1k)lqj duhas+m5 ;0xsw( is necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontally. What minimum se(df gjbopo3*l7 s,o(peed is required for the ball to clear g(js*,of( 3lebop7 odthe 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, flying2xp s k- t:m7hck;lfh2 a 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 still water is v . The boat is to make a qje zvf:b:/ pcl.m2 9feurf:( 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 mo/v.: cffu(z:pm9 jfeqe2l :b rving (a) upstream and back downstream, (b) directly across the river and back. We must assume u

  A projectile is launched from grou: /mv (fcgxc tyje/4*dnd level to the top of a cliff which is 195 m away and 155e :(/4/dmc fxj* vtycg m high (see
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 ofdu30k; ++my:,glz8ttu k0cwj9 iyk xx 2.10 m above the floor. The basket is 2.60 m above the floor. The player likes to shoot the ball at a 38.0 ;,umlkw3y 08d i9ct:kj+zuxxt k+0 yg$^{\circ}$ 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 aq gaizo(- j67v)6czmxs;: jy.f jps v4 $5.0-\mathrm{m}$ -high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine
( a ) her initial velocity, $ \overrightarrow{\mathbf{v}}_{0}$ ,    ${ }^{\circ} \text { above the horizontal }$
(b) the maximum height reached,   
(c) the velocity $ \overrightarrow{\mathbf{v}}_{\mathrm{f}}$ with which she enters the water.    $^{\circ} $ $\text { (below the horizontal) }$

  A stunt driver wants to make his car jump over eight cars parked side b b/ 4c+uhn8-frw msb.)y i+rmsy side bercy4sh s/muf+w)m- rb8+n.b i low 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 bat 0.90 m above the grgn zpm16 il; ordtlg;- zb*kw.a,kj9. ound at an anglg1; p6bd9lkk z,m- r.t;jogn*. ziwla e 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 speed of,ordg4;eq y u) $32 \mathrm{~m} / \mathrm{s}$ 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 thp (a d77ic48o25iqi oywn0z che top of a building with an initial velocity of 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart gun, and being a cleverwi lx;fo,q 8g, physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straightwl8ogqf,; xi, up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?