One car travels due easu2k8he/pbm 5 kt at and a second car travels north at Are their velocities eqe 85kmu/bkp h2ual? Explain.

Can you give several examples of an object’s motion in whichhjw6+ groo6:stoka /r58g **5aditfn a great distance is tra*5 h: n6oraswdk8ao it/org +56jtg*f veled but the displacement is zero?

Can the displacement vector for a particle moving in two dip8642ty ha daqn) 2xeomensions ever be longer than the length of path traveled by the particle over the sameo ah2 a)2q td84y6nepx 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 faw4dw0u:pdl) 7 0rxh $V_1=3.5\mathrm{km}$ 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 vector? Can three ud) p r;7kxldjiy-ac0 (nequal vectors? ic 0a;l-j (x)d7r pykdUnder what conditions?

Can the magnitude of a vector ever (a) be equal to :no g.f8osji2 one of its components, or (b) be less thanonjgio.8 2fs: 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, to get onja54opt/ 5gbz+;m 0j sn(c jfj a moving “car” the riders first hop onto a moving walkway and then ogj4bm0( nft5;zcjp/ jsj+a5onto the cars themselves. Why is this done?

If you are riding on a train that e(bdvce+ sp9-nt.6 ft cx3 ogi)k58svks :pg(speeds past another train moving in the same direction on an adjacent track, it appears kide+k cb pot(f.3p5s(-vs)gcse gn9 xt68v:that the other train is moving backward. Why?

If you stand motionless under an umbrella in a rainstorm where the drops fal0:tsu( tv ek(1,uyh vvl vertically, you remain relatively dry. However, if you start running, the rain begins to hit your legs even if they r v0thv,se((u:t ky1 vuemain under the umbrella. Why?

  A person sitting in an enclosed train car, moving at lh:svt4ko dvq4- 1a)dconstant velocity, throws a ball straight up into the air in her reference vd: 4 hq4a-l1vk os)dtframe.
(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 c(0 /cewtcm g ; 1uinrlb3nl3z7 h*d0euan row at the same speed in still water, set off across a river at the same time. A heads straight across and is pulled downstream somewhat by the current. The B heads upstream at an angle so as to arrive at a point opposite the starting point. Whi n lemcie(bl uhu3nw*1 dgrz0t7c; /30ch rower reaches the opposite side first? ----待选择----AB 

How do you think a basel336va.x4jvx ly ewf;ball player “judges” the flight of a fly ball? Which equation in thi. l3ew34jfxy a v;v6xls Chapter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the target? H3xpy/7 k*2khrysz(pfzjh8 ba8pm z;)ow should your angle of aim dependhyr2z/ s j;7f8b3z*( pkym)xakh z8pp on the distance to the target?

  A projectile is launched at an angle of err5 oqb6u5j6 ${30}^{\circ }$ 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 lm) i ,x2u0jerfrom the ground with identical initial speeds, but wixr 2 imjleu,)0th ${\theta }_{\mathrm{A}}$ 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 9cclm 31jqoz8 9kb4uc km southwest. What is the displacement of the car from the point of origin (magnitude and direm8uock4bq9jz3 c 9c l1ction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks gf .g :ujky(p;ez04*p l zw(ogsouth. What is its final displacement from the origin? Assume the blo(pg*yol0z(k:ejwz4;.pf gu g cks are equal length.    blocks

$$\begin{gathered} \text{ Show that the vector labeled "incorrect" in Fig. 3-6c is actually the difference of the two vectors. Is it } \\ {\overrightarrow{\mathbf{v}}}_2-{\overrightarrow{\mathbf{v}}}_1\text{, or }{\overrightarrow{\mathbf{v}}}_{\mathbf{1}}-{\overrightarrow{\mathbf{v}}}_{\mathbf{2}}? \end{gathered}$$

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

Graphically determine the resultant of the following three ve 4e hkz(fgr-nf;a02fp5/rx qector displacements: (1) /2ang(fr;z ekfef r05phq -x4$34\mathrm{m},{25}^{\circ }$ 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.ns 0yyyxxv78s43s2li c yo,nr $\overrightarrow{\mathbf{V}}$ can be written $(V_x,V_y,V_z)$ . 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)

$(a)V_{1x}$=   units $V_{1y}$=    units $V_{2x}$=    units $V_{2y}$=    units


$|{\overrightarrow{\mathbf{V}}}_1+{\overrightarrow{\mathbf{V}}}_2|$=   units $\theta$=  ${}^{\circ }$

  An airplane is travelinzz-cnf1nvex.q478 lqg $735\mathrm{km}/\mathrm{h}$ 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) $\mathrm{\Delta }{d}_{\text{north}}$=    $\mathrm{\Delta }{d}_{\text{west}}$ =   

  Three vectors are shown in Fig. below. Their magnitudes are given in arb--wbru269g r v4e xabpitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle wita rgwb62 bup-x 9ev4r-h 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+;smp 6qk2uys hic v kxjag7p).35 /hf $\overrightarrow{\mathbf{A}}$ and $\overrightarrow{\mathbf{B}}$ shown in Fig. below , determine $\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}$ . (b) Determine $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}$ without using your answer in (a) . Then compare your results and see if they are opposite.


$|\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}|$ =   
${\theta }_{B-A}$ =    ${}^{\circ }$above -x axis
$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|$ =   
$\theta$ =    ${}^{\circ }\text{ below }+x\text{ axis }$

  $\text{ For the vectors given in Fig. 3-32, determine (a) }\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}\text{, (b) }\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{C}}\text{, and (c) }\overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}\text{. }$




$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    ${}^{\circ }$ below +x axis
$|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    ${}^{\circ }$
$|\overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|$ =   
$\theta$ =    ${}^{\circ }$ below - x axis

  $\text{ For the vectors shown in Fig. below, determine (a) }\overrightarrow{\mathbf{B}}-2\overrightarrow{\mathbf{A}}\text{, (b) }2\overrightarrow{\mathbf{A}}-3\overrightarrow{\mathbf{B}}-2\overrightarrow{\mathbf{C}}\text{. }$



$|\overrightarrow{\mathbf{B}}-2\overrightarrow{\mathbf{A}}|$ =   
$\theta$ =    ${}^{\circ }$ below - x axis
$|2\overrightarrow{\mathbf{A}}-3\overrightarrow{\mathbf{B}}+2\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    ${}^{\circ }$ below + x axis

  The summit of a mountain, 2450 m above base camp, is mf85+wie3r( 5 ja gphoceasured on a map to be 4580 m hor3jo +f 5phar5 (cwg8eiizontally 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 magnitu- h70c96 :e5:i7j,ykjate 5xbbzndd yy gf*i yde of 70.0 units and a y component of What are the two possibilitie7:x-i5 yd jkcyihyeag,b 5z7ten* 6f0:9yd bjs for its x component? x = $\pm$   

  A tiger leaps horizontally from6 ;6w farrgy5bn53biw a 6.5-m-high rock with a speed of How far fromw yibf655a 3;rrgnb6w the base of the rock will she land?    m

  A diver running dives out horizontally from thzcwc )q.wll1q1w3nk 9e edge of a vertical cliff and 3.0 s latlqk z911lnqwcwc)3w. er reaches the 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 shoots water aca39p5j4is h- -t9;q3ul p(cwxrno xt t 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? Sketch thqtcxruwjt(;9li-c-3 sxo aph35 94 pn e two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, andb: 8x-y;gxds 7v sg;csa1 i;pd he wants the pebbles to dgxi;;x 1a-y7pbcss; :vdgs8 hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontally fro;g pfm5q.lxdqn1/ nn;urm .y x*kb7b. m the roof of a building 45.0 m tall and lands 24.0 m from the base. What was the ball’s initiaf1 ;q.gkr.lbbu/.m xm ; dy57pxnqnn* l speed?   

  A football is kicked at ground levelo g5s3 j),vwg-0b)dcxpgx;e u5uh igdu/ ,3ln with a speed of 18.0 $\mathrm{m}/\mathrm{s}$ at an angle of 35.0${}^{\circ }$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at f zjkhu(x; -hqr/7o.x from the roof of a building lands 36.0 m from the base of the building. How tall is the.zrkhh x-j(fx 7o/u;q building?    m

  An athlete executing a l+/eu nxwr,d 4fong jump leaves the ground at a 28.0${}^{\circ }$ angle and travels 7.80 m .
(a) What was the takeoff speed?   
(b) If this speed were increased by just 5.0 % , how much longer would the jump be?   

  Determine how much farther a person can jump on tyjk5m15wo0tx8tqkt3g y k-( j he Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravt5k(5 wkktg 31tyj xyjq -0o8mity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 7 s/92bdvybcgl8aro2q,ht 61c 5.0 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 t v/ld*b/qzv3a o flood victims isolated on a patch of land 160 m /bz alqv*v/3dbelow. The supplies should be dropped how many seconds before the plane is directly overhead?    s

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

  A projectile is fired with an initial speed of at an angle o(a gt+4hs,ncvf 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 grouaix 8stg ubm4eyo);0qg p1 19tnd level with an initial speed of at an angle of 37.0º with th1 at 4bu8it9qm ;gx0po )esgy1e 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 o y rsnrzb /d6.,k1m2g:ig3cbpf 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 px*vhi79bv*i m rojectile equal its maximum height?bi* 7vivx*mh9    $\circ$

Revisit Conceptual Example 3-7, and assume that the boy with thdz*i)2xw bay 5uod 6:qe slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show td2za owy)db* 65xu i:qhat 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 suppliec*(8 wqvky(vrw,ct9 is to isolated mountain climbers on a rocky ridge 235 m be( *ivtvw9(wc,yc8rkqlow. If the plane is traveling horizontally with a speed of 250 $\mathrm{km}/\mathrm{h}(69.4\mathrm{m}/\mathrm{s})$

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

  A person going for a morning jog on the deck of a cruise shic9ehnh n b;8ik8-n mec.wl) 1fp is running toward the bow e;nk9hc -hl81i fwn.) mec n8b(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 0.6 gbdel/ n 7o9vd.51kot*bk z6h0$\mathrm{m}/\mathrm{s}$ across his raft (that is, he walks perpendicular to the raft's motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.70$\mathrm{m}/\mathrm{s}$ relative to the river bank (Fig. 3-38). What is Huck's velocity (speed and direction) relative to the river bank?Magnitude =    Direction =    ${}^{\circ }$

  You are driving south on a highway at s p6phh3i5w /7ci+ov3d lz ph/f9gr 6c25 $\mathrm{m}/\mathrm{s}$ (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 2.30xes:meh-hlfv n+hz g 1w 782mfl 02*el$\mathrm{m}/\mathrm{s}$ 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 the x-evl0p a.+sdh)r f(6.kkatky spot each other when they are initially 11.0 km apart. How much time do the pilots have to take evar ks-k) xdha6t.lv eap+0.kf(sive action?    s

  An airplane is heading due south at a speed of 60gqi b v s5wrcuj4sv/t2t062 7gn ,o3dv0$\mathrm{km}/\mathrm{h}$. 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 sh 2ep nxax .qaq ga 5m1-f+c.dfcpa()7fould the pilot aim the plane in Problem 41 so that it will fly due south-d.+.1f aefcp nx5axc 2aqfm) 7qg( ap?    ${}^{\circ }$ east of south

  Determine the speed of the boat with respect to the shoe(y d wj ) 6ha3)w7,rk0 k+wpu+jhyaqkre in Example 3–11.   

  A passenger on a boat moving atkj qjyag;; 4g3j /kb(tpu6c7e.szmvd4i 8e3 z 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 water is t )6cle;-qly.zv 4ycf 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 watelt,ba( +i qu9ur 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 capableyv.xjp2 m,rc q. fn9(ihod7ax2 8)azj of 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 swimmi4z ws//u /.tvdlubyr))q8yf yng 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 spee7b)i-1o rwm 7pqertg5d 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,y( h rvpi ko(*2h ,y-0wxgh9sj 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 fu w564to bjmxv juxlif)8n ,+r-)p8i’s speed is not known. If the police car accelerates uniformly as given abovejn 6f xijpf)x-v, iu4tmblur58+8)w o, and overtakes the speeder after 7.00 s, what was the speeder’s speed?    km/h

  Two cars approach a street corner at right angles to each otherklkbq5 /b kw0, *ty+xl (Fig. below). Car 1 travels tq+x/ lklk,k *bb w0y5at 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 from anv cucw*hz.+y)we 58 ow:0s;prq 4k ex distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aim o:q)vw0w5 e8c +pck;uxn4yw.zh*ers 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 v w0zqcv)rv01 and 25 m south, and then takes an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumbz r q0cv)wv1v0er 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 rzz9x w,vy(n7( o42vnmvkhp)p oads, escape routes are sometimes placed to the side of the road for tr, w)9nxoh7vk4z(pm 2v(ypvn z ucks 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 component of a vector (in the x y planky*/4tn-c/ ,zby,0ck,x 0 *nb ec he)plnukgce) whose magnitude is 88.5 and whose ,e/b-zy)tn xpu ,4c0 k*g/h0bkn,* cyccnlkex 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 usgpzfp f 4sr9wn6w9irs 6. 92 $\theta ={30}^{\circ }$ with the vertical when viewed through a moving train window (Fig. below). If the speed of the train is $20m/s$ (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 tp:,xsc n* v-(rffdk .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 pi5s0 t,lh :jr$\mathrm{km}/\mathrm{h}$ 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 capabl .c +px 5r-0wtrfpzx6he of jumping 8.0 m . Assuming his horizontal speed is 9.16zxw- hrc0fpt +rp.x5 $\mathrm{m}/\mathrm{s}$ 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 andv4 0dx jb8s/uw1cm8cs 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 astronautmju1vcsxs 4/8b 08wcd 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 7.5a;p( .wt *qa 9:cypmik$-\mathrm{m}$ -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 abc rx dta c7 m(jy:aes3rs8o805*blw5fout 35 m above the water, but wb5l807oar m8(ys r:a*3c 5dcxjtsefthey 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 rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontjr*j 8; igbpnz z4;m,t/xz3fb ally. What minimum speed is required for the ball to clear the 0.90-mz *x,83ziznb/f ; bpj4 t;jgrm-high net about 15.0 m from the server if the ball is “launched” from a height of 2.50 m? $\approx$    Where will the ball land if it just clears the net (and will it be “good” in the sense that it lands within 7.0 m of the net)? How long will it be in the air? $\approx$    See Fig. below.

  Spymaster Paul, flying a constant adg vbye+rr.+/ ( yd-w $215\mathrm{km}/\mathrm{h}$ 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 . s(vcx4+5 ;5dyg q8 jhe/efzsp mybc2( 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 make5pd5zh;( g eems4 xv/cby (j2qcsyf +8 a round trip of total distance D if the boat makes the round trip by moving (a) upstream and back downstream, (b) directly across the river and back. We must assume u

  A projectile is launched from ground level to the top of a clim7 vgb, u6o,: jw4azbi-rgg- aff which is 195 m away and 15i6a- 4bg 7o-zvgrga :u, wjbm,5 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 of 2.10 m abovey cq39z1 zqh6a nbg.r/ the floor. The basket is 2.60 m .b3 9/nch1qaq rzgz6 yabove the floor. The player likes to shoot the ball at a 38.0${}^{\circ }$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22\mathrm{m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves the end of a mxsk.f bi/iz ayi8 z+f2.zqob01q 7)o $5.0-\mathrm{m}$ -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 by q*m .c*l/..mytir wztside below a horizontal rz.y.qm / rwt*li.c* mtamp

(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 tl5rql2(wnu eh/-vuwuy6 *b.l v:d.emhe ground at an angle u:umhr(qewv. l6y ube2.l v*wl dn-5/ 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 ahkkkht ob49tcw :17a k0z8/eu baseball with an initial speed of $32\mathrm{m}/\mathrm{s}$ at a ${55}^{\circ }$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of ${22}^{\circ }$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    ${}^{\circ }$