One car travels due east at and w(v i*m wn,v(wp+i-ok) q.v dma second car travels north at Are their velocities w q k+,mi(d(v.i*v-w)onpvm wequal? Explain.

Can you give several examples of an object’s motion in which a great distance twinocv2 s8( 5is traveled butcow82v s(in5 t the displacement is zero?

Can the displacement vector o ;qal92p2:45 2 jn7wgmn7g ywcubggj for a particle moving in two dimensions ever be longer than the length of path traveled by tl95n2 pcggu ;2ojy2 wa7b7qm n jw:g4ghe particle over the same time interval? Can it ever be less? Discuss.

$\text{ If }\overrightarrow{\mathbf{V}}={\overrightarrow{\mathbf{V}}}_1+{\overrightarrow{\mathbf{v}}}_2\text{, is }V\text{ necessarily greater than }{V}_1\text{ and/or }{V}_2\text{ ? Discuss. }$

  Two vectors have lengt,*w uz * xtkei+svrrq,n7-da)h $V_1=3.5\mathrm{km}$ 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 three6ahv/8 vj* 1yoders(z unequal vectors? Under what conditv6y (s 1azedo*h r/j8vions?

Can the magnitude of a vector ever (a) be equal to on1v b0k+kg;o fye of its components, or (b) be less than one of k+;k1 b0yofgv 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 -(sssv s g ,n8imgc.t:a moving “car” the riders first hop onto a moving walkway and then onto the cars themselves. Why is this g n(ss8ssgmt-: .i,vc done?

If you are riding on a train that speeds past another train moving in the samek-vw0 q 6en gnyghh6//f 9.w4e4z egj.e:zlzr direction on an adjacent track, it appears that the othe:hwj he6 ne4vzzw zg-9 rg ./qfekl4g60.y ne/r train is moving backward. Why?

If you stand motionless under an umbrella in a rainstorm whe0bdix/ m*o6tvrgjwj38c;ny; f/ y8tx re the drops fall vertically, you remain re ;n y i 6xgo*3tf/8rw;cj 8/vmx0jbtdylatively 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 at constant vel4e e i:qrn2jal3.rf(pocity, throws a ball strae efj.q rr:na2ip4l3 (ight up into the air in her reference frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row at the same speed in still water, set offyae*-kqs/m t2de 29 bm 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 steek*2y m92 -adm qb/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 fa .bjx8;zfb9s.r u 1la fly ball? Which equation in this Clab bf.j1;s .f89rzuxhapter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the target? How shou6w+ep-i qekkaw0 djk8h8 3ec*ld your angle of aim depend on the distanc eei a*3wwpj+hkq-ke kc06 88de to the target?

  A projectile is launched at an 8mnyll- 90mwo 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 th6t u my0nd:7jbe ground with identical initial speeds, but bdyun 07tj m:6with ${\theta }_{\mathrm{A}}$ larger than ${\theta }_{\mathrm{B}}$
(a)Which cannonball reaches a higher elevation? ----待选择----AB 
(b) Which stays longer in the air?  ----待选择----AB 
(c) Which travels farther? If the angle of a is 40 ${}^{\circ }$ the angle of b is 30${}^{\circ }$  ----待选择----AB 

A car is driven 215 km west and then 85 km southwest. What is the di 1c yf :r.dj +cr73lyes7hpz.ssplacement of the car from the point of origin (magnitude and direction)? Draw a di1 z7s3fdclypjhc .eryr .s+:7agram.

  A delivery truck travels 18 blocks north, 10 bloze nr y(h;*lxd( e(xu*s) 5pvncks east, and 16 blocks south. What is its final displacement from the origin? Assume the blocks are equal l(*x;pndr) e(u vysz5n*ex h (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 tg7 v l3osar.7yhree vector displacements: (ls7.r3 7oavgy1) $34\mathrm{m},{25}^{\circ }$ 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 vector , sl6v-x4g aoxo85lnr*ql s-t$\overrightarrow{\mathbf{V}}$ 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 traveling (gx,j lrtsm1po7e)5.s9nlx k $735\mathrm{km}/\mathrm{h}$ 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 magnitu. x.gx*yomfn /des are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) xmof. n.g* y/xcomponents, (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 vector3y rd2k1n lm hy:g6k5+r9k bees $\overrightarrow{\mathbf{A}}$ 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 measured on a map to b3r1mg y4j; ogowo b6/xe 45806bmw1r /ojo3x;4 ggoy m horizontally 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 thatp )vov ,)t0,qinh4 iuo has a magnitude of 70.0 units and a y component of What are the two possibilities vovpq 4i itho)un,0 ),for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a speed of How far:j5h i bhw1yw5o i :ewfs,rz6. fromhez5wib w f5. ,o61: wh:rysji the base of the rock will she land?    m

  A diver running dives out horizontally from the edge oz;t 37emdk *27ozknr tf a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its base did the diver hit the water? tnk o73zkr2zd*;7met high of cliff is    the distance is   

A fire hose held near the groundssg-hjt 8+eu/ ww 2qv3p*pf-s shoots water at a speed of At what angle(s) should *s-+f-pgeuvswtpw q/j8h 3 2sthe 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 Jun/g*mq 9n5b fkliet’s window, and he wants the pebbles to hit the window with only a horizontal component of v m g*5bfq9nkn/elocity. 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 frbm23pk :t8 te+38 twmxuv-tsfom the roof of a building 45.0 m tall and lands 24.b8 3tmu2t :ek3t-sxftvw8+p m0 m from the base. What was the ball’s initial speed?   

  A football is kicked at ground lo;a*0iagpg p 3phk*zp6 go-5level 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 a building lands 36.0 m b:svjtm+1 xdizlikst/ m).51 from the base of the builbtlz1sv1d +is.)txj m i:/mk 5ding. How tall is the building?    m

  An athlete executing a long jump leaveswfn,r7tr x owp x)5;4: s25bjycmpug.m4g5 lc 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 favnotp1 ns ;r ot/i*;ud9+ 5cbzrther a person can jump on the Moon as compared to the Earth if the takeoff speed and angle are the same. The accelerari5+s1c9;pn dtb /vzno ;t*oution due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on t4)( zbo7rs 9cf/gp;ht 8.i1urhhv ptihe 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 to7q jy +k1y(rpa+uu4fc.rkoli+-gi k9 flood victims isolated on a patch of land 160 m below. The supplies should be rgpu.j(41o+y kaq7y +kil fcrk -+i 9udropped 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 wita*b4 d x1 xsvg+35,g9hwdl+oe -gbh ahh 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 zot8: +8bumfe0 :sndb from the edge of a cliff 125 m above ground level with an initial speed of at an angle of 37.0º with tbnbz 8sof0 8 ed:tum:+he horizontal, as shown in Fig. below.
(a) Determine the time taken by the projectile to hit point P at ground level.   
(b) Determine the range X of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point P, find   
(c) the horizontal and the vertical components of its velocity,   
(d) the magnitude of the velocity, and   
(e) the angle made by the velocity vector with the horizontal.    ${}^{\circ }$ below the horizon
(f) Find the maximum height above the cliff top reached by the projectile.   

  A shotputter throws the shot with an initial speed of m es5k5m0k 9r.qh/h gb(5 vicj 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 maximum heigk9w l;qpzah+v4, duz. zp 13ixaw z84iht .zqv3uaix9zzp,l;4kzdw4ia+1 ph w 8?    $\circ$

Revisit Conceptual Example 3-7, and assume that the boye5s1z sbf8 s,bng2 c +(hqnaf)1 chsc+ 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 letting go at the moment the water bbhf+gz5ns )1sbs cf8qnas(1c2+ e hc,alloon is shot.

  A rescue plane wants to drop supplies to isolated mountain climbers gj(98gs z ra4aa);omb on a rocky ridge 235 m below. If the plane is travelo8r a9 mjagsg);ab (z4ing 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 cpw0 :kdo p;fpn-zn ;dae0yen* ek7m2/ ruise ship is running toward the bmpwznn*e0eky:; o27f - d/;0ekpan dpow (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 (o3sen4 (s: o+hyiltx :qpgsv70wpl; 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 hr -wqsqhda*6( im 2aa;ighway 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 c,dxmqa5xx ymx+p: 3: h8sc-s.30$\mathrm{m}/\mathrm{s}$ in still water.
(a) If the boat points its prow directly across a stream whose current is 1.20$\mathrm{m}/\mathrm{s}$ , what is the velocity (magnitude and direction) of the boat relative to the shore? magnitude    direction    ${}^{\circ }$
(b) What will be the position of the boat, relative to its point of origin, after 3.00 s? (See Fig. below)diraction =    awayfrom the starting point,angle =    ${}^{\circ }$ relative to the shore

  Two planes approach each other hev0mia:e mo, a1ad-on. Each has a speed of and they spot each other when they are initially 11.0 km apart. How much time do the pilots have to take evasivv mo0ae, i1ma:e action?    s

  An airplane is headic18.idbx 1n-h lupmn3 ng due south at a speed of 600$\mathrm{km}/\mathrm{h}$. If a wind begins blowing from the southwest at a speed of 100 $\mathrm{km}/\mathrm{h}$ (average), calculate:
(a) the velocity (magnitude and direction) of the plane relative to the ground, and    ${}^{\circ }$ east of south
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.   
[Hint: First draw a diagram.]

  In what direction should the pilot aim thexxa3qe7nn 6(hopw5o10 o:m itj+ o+yk plane in Problem 41 so that it will fly duem oi3n:kaopow 6+ 7( 0 yxqn1o5ehjt+x south?    ${}^{\circ }$ east of south

  Determine the speed of the boat with respect to the shore in Examplcrr(5f + .aybue 3–11.   

  A passenger on a boat moving anob7dcvmy1r8 o )8p.zr )rk8ct 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 waz 3g j3,l.xmnmzv5;xz1c01p pjt1rvpter is 2.60 $\mathrm{m}/\mathrm{s}$ must aim upstream at an angle of 28.5${}^{\circ }$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current?   
(b) What is the resultant speed of the boat with respect to the shore?   

  A boat, whose speed in still water is 1.70 : ,i:tisxe h6a$\mathrm{m}/\mathrm{s}$, 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 ki7)s q;qxn1ew xo a+*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 swimming 0jn ,sbpx0vq4082+a ux pbod* bztv 60g.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 isu9sfm-2p oz+d lj:xfd,n/k e5 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 )3sw kcmxjeu+4 cd1 w9e,f) cva 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 poligj,r g/1 r.bjvm.k1hqp+l t3s,ks 86rr8rxcr ce car accelerates uniformsj1 qrbr,k,rr3cj 1tv mgpx/kr8. .6r l +s8ghly 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 qw dfr0wj;m04at right angles to each other (Fig. below). Car 1 travels at a spf r dwj4qw0m;0eed 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 hg)iszflw4+:x it8;wd iz2q- wead from a distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At wh wi4wz)2wt:z f xqigs8d+l-i; at 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 tr:bbf+2u*pd8p vz a6 donr)/ucuck, 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 horizontal planes. Assume x is east, y is north, and 8pvpcun6u dr/)z+d:2fba* ob 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 rr1m5/z(ical c outes are sometimes placed to the side of the road for trucks whose brakes might faci /m(r5z1lca il. 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 ns4txht h( c3qa*l9v )of a vector (in the x y plane) whose magnitude is 88.5 and whosenlht sqc*9 ( 4tvxah3) x 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 anntnwwjy.b,r9q3rn2 2awdgx bs 4g 16 ,gle $\theta ={30}^{\circ }$ 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 withfp6tx n .hg mf 7wv)o6xnof5;3 a speed of 155$\mathrm{km}/\mathrm{h}$ relative to still air. After 1.00 hour, the pilot notices that they have covered only 125 km and their direction is not south but southeast $\left({45.0}^{\circ }\right)$. What is the wind velocity? $v_{wind}$ =    km/h $\text{ The direction of the wind is }\theta$=    ${}^{\circ }$ north of east

A car moving at 95 rxa de5q4od5 s+ n*;uu$\mathrm{km}/\mathrm{h}$ 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 jumpiby7+ ig*8yu bnng 8.0 m . Assuming his horizontal speed is 9n gbb7uy8y+*i.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 2*,uqg:i 4 vere: x4awjulvr :a “nine iron” to the Moon and hit a golf ball about 180 m! Assuming that the swing, launch angle, and so on, were the same as on Earth 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 bothr:a :iluuv,4vexrj*e:4 g w2 q cases, but on the Moon there is none!) g${}_{moon}$  

  When Babe Ruth hit a homeenqo0:zl 3a,nr 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 horizontalqlxc8qk - kkn 37m+n2yly from rock platforms about 35 m above the water, but they must clear rocky outcrops at water level th+3cl2 mqnn7yk q k8kx-at 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. W-e1c(oa5(nbxbq 2kw chat minimum speed is required for the ball to cbxc b2(w1qk(n e5a -oclear 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 constanaslr s*- p7lyi o12ak0t $215\mathrm{km}/\mathrm{h}$ 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 a0erhlei1 ;mpq1/ j9sis v . The boat is to make a round trip in a river whose current travels at speed u . Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving (1j e;1rli mhs9pqa0/ea) 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 cliff which + 4 eu; ajb6pfr-e olei930wac)abh5yis 195 m away and 155 m high +3) abwl euo0ra-ae45;9yjcpf h ebi6 (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 above the floo h thdow1lrqm2838:c63bsm lyr. The basket is 2.60 m above dsl q6:l 8rcwmhmh3y82t 3o1bthe 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 z2sp91fv( bcdhzqi0 - $5.0-\mathrm{m}$ -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 b6yfcauq ir p*t,i 62+by side below a hor +6ryaii6u, 2*bc qptfizontal ramp

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

  A batter hits a fly ball which leaves the bat 0.90 m above the ground at an angv4 zze:ki:x d wki,.o 4+c.agile ofk i cw:kigxd4 a:i.+v,.zo4ze ${61}^{\circ }$ 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.