One car travels due east at and a se,8 voh3 btfg1 nf1k. jit. -mzcyc.d7acond car travels north at Are their velocities equal?gh, t.fc178c.1o k.f- yzbn3ma di jtv Explain.

Can you give several examples of anotu(n:/ yr btl/2iad/ object’s motion in which a great distance is traveled but theoi t:dbl( r //a/tuyn2 displacement is zero?

Can the displacement vectxu t.r md-7lb+bcd 2.aor for a particle moving in two dimensions ever be longer than the length of path traveled by the particle over t.7 ml td ub-rbadcx.+2he 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 lenim(h4z mt)d28w gr ,yugth $V_1=3.5\mathrm{km}$ and $V_2=4.0\mathrm{km}$ . What are the maximum and minimum magnitudes of their vector sum?max =    min =   

Can two vectors of unequals g8;(m zra:im magnitude add up to give the zero vector? Can three unequal vectors? Undemsmzg 8a;:r(ir what conditions?

Can the magnitude of a vector ever (a) be equal to one of its components, orw4 hmij *+: nq2rpacj( (b) be less than on*(a pj nwic4jr qh2m:+e 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 on a moving “car” the rjzwo. ( j3r1nbiders first hop onto a moving walkway and then onto the cars tbo3jw r n(j.1zhemselves. Why is this done?

If you are riding on a train that speeds past another train movin zn n667sbv(tcg in the same direction on an adjacent track, it appears that the other trainsn(z6bn6t cv7 is moving backward. Why?

If you stand motionless under an umbrell.eua/n926ydpx*5 ssa v(mt uxpfg ;0* o*j ykha in a rainstorm where the drops fall vertically, you rt*y;6pes snjayf u5pa 9k* h2 xg*.m(uo0 dx/vemain relatively dry. However, if you start running, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an enclosed train car, moving atn)w3gob zi51zti7 k9 y constant velocity, throws a ball straight up intynw3bz1o9 )k75 igzti 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 samelgb4 zd24h;c9xh0,b 3dlq7 a7pf lol m speed in still water, set off across a river at the same time. A heads straight across and is pulled downstream somewhat by th0,qlp 4b3czdla ;lb27f gl9 h4dxm7ohe current. The B heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reaches the opposite side first? ----待选择----AB 

How do you think a baseball player “judges” the flight of a fly ball? Which eqx; u1(e gr49 akihzs:x8;oul uuation in th h91alg8;; xxzs 4iueo:(ruukis Chapter becomes part of the player’s intuition?

In archery, should the arrow be aim58kkmaibowfwnj /t m17/) c(zm -ozp,ed directly at the target? How should your angle of aim depend pjm k) z/w(kmonft7m c5 z,8abo/ i1w-on the distance to the target?

  A projectile is launched at an angle o f* 8w kq*.puw::xgmoyf ${30}^{\circ }$ to the horizontal with a speed of $30\mathrm{m}/\mathrm{s}$. How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch?   

  Two cannonballs, A and B , are fired from the ground wiy-5kq ,2woe msth identical initial speedy , 5qkmoe-2sws, 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 andx bo f.(*rvc:* *ndc6ab- txmu then 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)? Dra:n-ar dm*(xbc*cb6.o tfu*v xw a diagram.

  A delivery truck travels jpo)m ynsu2uy2 r))uvn*2gl3 w-by4 n18 blocks north, 10 blocks east, and 16 blocks south. What is its final displacement from the origin? Assum n)sgr 4vlub-n2u jy) yu2own32)m* pye the blocks 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 threeu8 i7u- plr(fc vector displacements:u8i-ur( cf7l p (1) $34\mathrm{m},{25}^{\circ }$ north of east; (2) $48\mathrm{m},{33}^{\circ }$ east of north; and (3) $22\mathrm{m},{56}^{\circ }$ west of south.

  The components of a vect-9y/2xv,honbh xrl n/. /zqcd or $\overrightarrow{\mathbf{V}}$ 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 travei9vmni( e /b+hling $735\mathrm{km}/\mathrm{h}$ 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 int3mt) 7sl x)3vmb v49irb5 xdo arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) co9rxt3)b m74vlx3ts mb5)oid vmponents, (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 7) ju0*oahfqq4yo 5yx$\overrightarrow{\mathbf{A}}$ 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,xfvt/2 w rp(on-jh1aemi91z2 is measured on a map to be 4580 m horizontally i(jwe xfrzo1/nha2p -12m9tv 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 p7qegc,xh opc(9 swq ))cf;ow.lane that has a magnitude of 70.0 units and a y component of What are the two p.7w9 exoqowc),gqc (; c)hfspossibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a speed of Ho)oet2s :b us4tw far from the base of the r4b:ss )eutot2 ock will she land?    m

  A diver running dives out horizontally from the edge of a vertical3;(eu jbsl a;;377hblrva rjd cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its base dida s j;7 ue(lhdb 3;7b;j3rrvla the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots waupg1idy j x2u.xk/4igw94s+f4g; fezter at a speed of At what angle(s) should the ku p4+xswig 4/;g4 9ef uzidx1 j2gyf.nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, and he wants the pebbles:ocak0z ;ny p3 to 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 :ykc 0oa3nz ;pwindow?    m/s

  A ball is thrown horizontally from the roof of a building 45.0 m taluer1e0 h eswk 4c-iy58l and lands 24.0 m from the base. What was the balw4u05rcek e1 sei8y-h l’s initial speed?   

  A football is kicked at gbhd,5 l7 ybq yx.:fpv7ax16 qnround level 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 from the roof of bnpu1wf4 7/h3s2po8ob saf*w a building lands 36.0 m from the base of the building. How t8pa7bo3fowsh1w2u s*4bf/ npall is the building?    m

  An athlete executing a long jump leaves the ground at a pz1k6m6hf ham:0kpw) 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 fartntylyk+3/5txuv wf:4rmp4vs3 b.n * j her a person can jump on the Moon as compared to the Earth if the takeoff speed and angle are 3wn.s4*yb43/ tjtmkrunfp5 x y :vl +vthe same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly aosc2gdjv m/m j6 62dg qctb3287qhh 1ut a 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 su +dnvt ct/8slbky8m1*/. akvupplies to flood victims isolated on a patch of land 160 m below. The suppliey1*kudbl av+8smt /k/c nt8 .vs 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 withz5*c akbj5kt0 3dl66fp .f spr an initial speed of at an angle of 34.5${}^{\circ }$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot from the edge of a cliff 125 m above ground lerw.s8jkp27 ab*z:mw (ag zr )lgze*q /vel with an initial speed of at an angle of 37.0º with the horizontal, as shown in2.*8wr )zr gak7*apmbwl(/zg : sqezj 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 inizbo4y6cph j9o-9vyy ko2/0d xtial 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 projecti :2cw tb9buq0( jpkv/- ibi-yule equal its maximum height?/ -0w ybbijiq2 : pk-utvb(9uc    $\circ$

Revisit Conceptual Example 3-7, and assume that the boy with the slingshot isosg::4.)2a i8(+nm-d sz jukt4dn7e acshli u below the boy in 4e n tjss(uu a a:7oi+g)2l n-dk:idzhm4s8. cthe tree (Fig. 3-36), and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants t (c8,m.fwljd ya c8w( ub(eh5no drop supplies to isolated mountain climbers on a rocky ridge 235 m be d8(uywal(n ch , 8jb.w(fme5clow. 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 iwnv))n,r96 eotlg i .a0c;yy of a cruise ship is running toward the bow (front) o 6rn),i9l);yovte y 0ciwg.an f 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.zea rs/ 6vxf:d16 y)ro60$\mathrm{m}/\mathrm{s}$ 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 2e)ruu t-9qt es5)vnw)5 $\mathrm{m}/\mathrm{s}$ (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 2l emh ozdxdz1q7.6-a* s; o8x7bp nt;z.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 e2wu4 i -dkf2tfpn (kj.ach other head-on. Each has a speed of and they spot each other when they are initially 11.0 km apart.t( 2if 2n4fjwukp kd.- How much time do the pilots have to take evasive action?    s

  An airplane is heading due south at a speed of 6ic4gpwys:9+7 :-xxrbosnx m g+6 ado600$\mathrm{km}/\mathrm{h}$. If a wind begins blowing from the southwest at a speed of 100 $\mathrm{km}/\mathrm{h}$ (average), calculate:
(a) the velocity (magnitude and direction) of the plane relative to the ground, and    ${}^{\circ }$ east of south
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.   
[Hint: First draw a diagram.]

  In what direction should the pilot aim the plane i) 7xssay:.t3pehci0gryo) w-n Problem 41 so that it will flyxtopsri wh c 0.3e)s -)agy7y: due south?    ${}^{\circ }$ east of south

  Determine the speed of the boat wit6 qum7; xrf: -ukzebl.fn/ lm;h respect to the shore in Example 3–11.   

  A passenger on a boat mml: /emqff06o oving at 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 skm nmzl 9 i)5wdwufr0(2+ch.ktill 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 stinjy pg zz 10i9ng9tu90ll water is 1.70 $\mathrm{m}/\mathrm{s}$, must cross a $260-\mathrm{m}$ -wide river and arrive at a point 110 m upstream from where it starts (Fig. below). To do so, the pilot must head the boat at a 45${}^{\circ }$ upstream angle.


What is the speed of the river's current?   

  A swimmer is capable of swimming 0lbmd,1+ yfqv9a6ns 3 0nfck s0.45 $\mathrm{m}/\mathrm{s}$ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{m}/\mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?   
(b) How long will it take her to reach the other side?   

  A swimmer is capable of swimming lq+v)(n 7vpva90 v* sd7kcnru 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 is 620 za3c9n 8h6awn$\mathrm{km}/\mathrm{h}$ 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,zcd 2wc f.)t1e 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 polih 4dx+74gs-o ieqql16h8b (hkl(lcpvce car acxbk+l vc74( 1lei lsgd(hho 48qqp6 -hcelerates uniformly as given above, 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 other (Fig. below). Ca +tizh9cg09 p8z) wzkwr 1 travels at a speedh0p+ )zwzct8i9wz 9kg 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 a distance: xtriuj:6zm f0a n05s of 27 m . When William aims directly at the apple, the arrow is horizontal. At what anglem:rnu0tf 0z65: sjiax 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 truckb165w 3be(a lbmuz7mv , walks 50 m east 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 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 horizonta mm e13z ub57b(w6lvbal 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 route /0k+po4(n(0c/sbf mcder8 -6dgmhu dvv as,js are sometimes placed to the side of the road for trucks whose brakes might f ba/es cp-( gr8kd ,+vnmsju m/06(4oddfchv0ail. Assuming a constant upward slope of 32${}^{\circ }$ , calculate the horizontal and vertical components of the acceleration of a truck that slowed from 120 $\mathrm{km}/\mathrm{h}$ to rest in 6.0 s . See Fig. below

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

  What is the y component of a vector (in the x y plane) whose magni 41k5at gthfutn;:f-wtude is 88.5 and whose x comh-4f akut 1 t:tfw5n;gponent 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 anglb9rem rwbb5;2e $\theta ={30}^{\circ }$ 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 speedig+q6jnf2w;i(tk )h084,giohu fotm 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 k3aaqpis7 s c.ff)y7dyf3;+g$\mathrm{km}/\mathrm{h}$ passes a 1.00$-\mathrm{km}$-long train traveling in the same direction on a track that is parallel to the road. If the speed of the train is 75$\mathrm{km}/\mathrm{h}$, how long does it take the car to pass the train, and how far will the car have traveled in this time? What are the results if the car and train are instead traveling in opposite directions?

  An Olympic long jumper is capable of jumping 8fg nl0g y*-rc73j q6sh.0 m . Assuming his horizontal speed is 9.1s *6cl3g 07yhn fj-qrg $\mathrm{m}/\mathrm{s}$ 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 tcnke7w10)5co+ozo wr 2 c 3xqjhe Moon and hit a golf ball about 180 m! Assuming tha 7erkoo1jwz5+oc) 2 cn 3wc0qxt 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 resistance in both cases, but on the Moon there is none!) g${}_{moon}$  

  When Babe Ruth hit a homer ors 9s l-/ne:w dya4cv;ver 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 horizontallf 4 rmd(h /er.s19prdjy from rock platforms about 35 m abovedj /f4dh9e.p( sr1 mrr 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 rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontally. What minimum5qpkg/.cf e vu fw+g;:zjlj 219 ad-md speed is required for the ball to +ga1/l:.q-de92pjm5gkucw;fv j df zclear 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 a uf 6q.)d7p 0c6nvmqkwe9 h(wu8s6v,e,d bikiconstant $215\mathrm{km}/\mathrm{h}$ 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 boatyldify53v6h(k ;kp-n2 o pf/ u 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 roun-;o /plfp 3ndv6yfyk(h2 u 5kid 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 q;e3kimu-y u0gu5j 0 jo,f7s/mldm1uof a cliff which is 195 m away 1uiu7kdfymjm g3uums q-ol5 ,/0e 0;jand 155 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 cb: ;,bi-zy pgyyes 7*m above the floor. The basket is 2.60 m above the floor. The player likes to shoot bb,z y;ye :gyi*spc7- 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 0+ ut m0srf90mh+yu bwa $5.0-\mathrm{m}$ -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, tjtz5 rlqa-:hmmo1ggz+;,cnyhp74 side by side below a horizontal,zymj 1 p-tt+c rhm5 7gh4goq:zn,;la 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 ba-wf2n enny)ukbv0/, a t 0.90 m above the ground at an angle )2kw,y n0nuefvnab -/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.