One car travels due east at and a secon 27de iei ;gj,/dz4cnbd car travels north at Are their velocities equal? E2, ib;ecz dgd/ine47 jxplain.

Can you give several examplb n(w9 f26pq 6/hrm68osxc xames of an object’s motion in which a great distance is traveled but the displacemen/o8m amsp r66cw9n 6fx2q b(hxt is zero?

Can the displacement vector for a particle moving in two dimensions evy3s ksr8pfj6na7 nv vh ,;z-)yer be longer than the length of pa) rpy6kz a7vnv- ,snfyshj3;8th traveled by the particle over the same time interval? Can it ever be less? Discuss.

$\text { If } \overrightarrow{\mathbf{V}}=\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{v}}_{2} \text {, is } V \text { necessarily greater than } V_{1} \text { and/or } V_{2} \text { ? Discuss. }$

  Two vectors have lengt 8 qntw9xn ph,)t+ex0sh $ 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 magnitu)*n3 r06 asw fx77q:vwjlea u0wysr5pde add up to give the zero vector? Can three unej7ss 0 0 q7wfvrlu6yewp3a )nx5a rw:*qual vectors? Under what conditions?

Can the magnitude of awu3m2n5 wuac*sv bhf, xi 5b2h-b gku5v9 .2ak vector ever (a) be equal to one of its components, or (b) be less than one of its componentnu k52 -*cgmvfib 5wx3v9ab. swu hb52h,uka2s?

  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 gel;oi4k . pxb*rgbv b*4cen6 :st on a moving “car” the riders first hop onto a moving walkway and then onto the cars themseli* e ;b6.c:kg vbr4lbsox *4pnves. Why is this done?

If you are riding on a train that+*:h c0k .d epjvh6cwf speeds past another train moving in the same direction on6 cek:+c0jdv hf. hw*p an adjacent track, it appears that the other train is moving backward. Why?

If you stand motionless under an umbrella in a rainstorm where the drops fall x(kekejj pd/o34zx03 8to0yb vertical(j3bjdk0 pox 4xe3yk oe/08tzly, you remain 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 at co t 7gw2xv-o7+y 8wlxrbnstant velocity, throws a ball straight up into the air in her referenv+gxw- xr 87tyo l72bwce 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 spee3hpmdj 6nqd+va /c c5 q75jlv)d in still water, set off across a river at the same time. A heads straight across and is pulled downstream somewhat by the current. 5 aj6vl/)hqjq+3nd7 m 5cvpcdThe 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 “judgeqaxl kp9 my)83 )tn0ils” the flight of a fly ball? Which equation in this Chapter becomes part of the player’s intuition qny89aklil) ) p0mtx3?

In archery, should the arrow be aimed directly at the target je)l j+5:ujzp? How should your angle ofup+5 ezlj:)j j aim depend on the distance to the target?

  A projectile is launched at an angle(3 gz+*kqhd -posh); el 7zmfo 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 7 xtmvn.-g,rk0 plo m8from the ground with identical initial speeds, but wirxvm,gp o0t- mk7n.8lth $ \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. Wha cs4 j5j;)nrtdt is the displacement of the car fromj cdr;)sjn5 t4 the point of origin (magnitude and direction)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks south. ppavpz-f2s 0( qmy3;n What is its final displacement from the origin? Assume the blocks 3q spny z am(02fpvp-;are equal length.    blocks

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

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

Graphically determine .elb- nwi-3ya nl+g4dthe resultant of the following three vector displacements: (1)dnl w.yg-+ae4n3-ilb $ 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 (fnt : lc( a3u.ehp sgm5+hofjb0owr+h :b7t1 $\overrightarrow{\mathbf{V}}$ can be written $ \left(V_{x}, V_{y}, V_{z}\right)$ . What are the components and length of a vector which is the sum of the two vectors, $ \overrightarrow{\mathbf{V}}_{1} $ and $\overrightarrow{\mathbf{V}}_{2}$ , whose components are (8.0,-3.7,0.0) and (3.9,-8.1,-4.4) ? components (a,b,c) a =    b =    c =   
length   

  $\overrightarrow{\mathbf{V}}$ is a vector 14.3 units in magnitude and points at an angle of $34.8^{\circ} $ above the negative x axis.
(a) Sketch this vector.
(b) Find $V_{x}$ and $V_{y}$ .$V_{x}$ =    $V_{y}$ =   
(c) Use $ V_{x}$ and $ V_{y}$ to obtain (again) the magnitude and direction of $\overrightarrow{\mathbf{V}}$ . magnitude =    direction =    $^{\circ}$ above - the x axis
[Note: Part (c) is a good way to check if you've resolved your vector correctly.]

  Vector $\overrightarrow{\mathbf{V}}_{1}$ is 6.6 units long and points along the negative x axis. Vector $\overrightarrow{\mathbf{V}}_{2} $ is 8.5 units long and points at $+45^{\circ}$ to the positive x axis. (a) What are the x and y components of each vector? (b) Determine the sum $\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{V}}_{2}$ (magnitude and angle)

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


$\left|\overrightarrow{\mathbf{V}}_{1}+\overrightarrow{\mathbf{V}}_{2}\right|$=   units $ \quad \theta$=  $^{\circ}$

  An airplane is travelihp4tbpr ) )ha7ng $735 \mathrm{~km} / \mathrm{h}$ in a direction $ 41.5^{\circ} $ west of north (Fig. 3-31). (a) Find the components of the velocity vector in the northerly and westerly directions. (b) How far north and how far west has the plane traveled after 3.00 h ?(a ) $ v_{\text {north }} $=   $v_{\text {west }} $=    (b) $\Delta d_{\text {north}} $=    $\Delta d_{\text {west}}$ =   

  Three vectors are shown in F. hbmrs3jd1 q*ig. below. Their magnitudes are given in arbitrary units. Determine the sum of . *q1s3db jrhmthe three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with the x axis.


$(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}})_{x}$ =   
$(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}})_{y}$ =   
$|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$

  $\text { Determine the vector } \overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{C}} \text {, given the vectors } \overrightarrow{\mathbf{A}} \text { and } \overrightarrow{\mathbf{C}} \text { in Fig. below}$



$|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{C}}|$ =   
$\theta$ =    $^{\circ}$

  (a) Given the vectors,,t3e1du/ oiel,cbao $ \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 obk 2 (iw(en b4(jesi/base camp, is measured on a map to be 4580 m h4eb esk b(/i(in2o(wjorizontally 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 t*c 4iei8 pdvs*he xy plane that has a magnitude of 70.0 units and a y component of What are the two possibilities fcse* 4iipd8v* or its x component? x = $\pm$   

  A tiger leaps horizonta,kf8sd j a1n/; yw3hvo ;hqz;illy from a 6.5-m-high rock with a speed of How far from the base of the rock widw 13hy,if;/sanjz k ho;qv8 ;ll she land?    m

  A diver running dives out horizontally from the edge of a4jlq-wr eb7kq43,olxe xv.crdvib:8 s. 0q -j vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its base did e-:qx.04e,brq4kq- vv x sld8joj7cwli3r b . the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots water at a spe4p/k*um ep*z + dokav9ed of At what angle(s) should the nozzle point in o*v oma4 *kzup9/pe+kdrder 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 cx-371 dr9qj pp*aev yJuliet’s window, and he wants the pebbles to hit t3px9 drp1* eq7 ja-ycvhe 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 from the roo(krb.9 zufm ;u -fgw6if of a building 45.0 m tall and lands 24.0f i.(ur-;fwu bm 9z6gk m from the base. What was the ball’s initial speed?   

  A football is kicked8 gp8)-d s mq;eujtah) at ground 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 horizoc qa0bv+j ;vjpgcq l6:9r9+dontally at from the roof of a building lands 36.0 m from the base of the building. How tall is the build+ p0;gqqla c9j v+ :ov96drjbcing?    m

  An athlete executing a long jump leaves the ground at ajms;w1o7 ukm c5 /nna( 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 c2ji.vj)aq; zgo 4 7leqan jump on the Moon as compared to the Earth if the takeoff speez47) lq;vegaji2.jo qd and angle are the same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly ,3i ik sgx5vh5nw5.ith 2a33 sagcjp6at 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 supplies to floo1k sii;hby 6e 949)fg dz1w5lbilk larpk32b *d victims isolated on a patch of land 160 m below. The supplies should be dropped how manl5 khb i b96)4yi1w2*lkb i9dzp1eafrg 3 lks;y 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 withu2 fa3djv-c: y 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 the96jh0u r5iusyqo qsgv9 0f(i-n pl .1z edge of a cliff 125 m above ground level with an initial speed of at an angle of 37.0º with the horizontal, as shown iq519.fqrzou(ilu-s yiph 6s9 0 jngv0n 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 initiagaj p x+).s1; mzic1gf7g)ltnl 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*z6)ee k.y8dlzmv/ anom9 *pfk. f bh/ range of a projectile equal its maximum heightk 8 .amhb9/*vk z. zofnpyf6el/de) *m?    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with th6a1vdizg .1fz7v4wrq pj e09ie slingshot is below the boy in the tree (Fig. 3-36), and so aims upward, directly at the boy in the t9v1ziv7az6e.i14 j f rdqwpg0ree. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon is shot.

  A rescue plane wants to drop supplies to isolaterz/okil 0b 7x2tiz7uq z;5 f+td mountain climbers on a rocky ridge 235 m i+/ f7r zzz2 txlti75k;o0ubqbelow. 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 morningu. ggml/ (uk.bl kgdfza6*p :1 jog on the deck of a cruise ship is running toward the bow (f*kgkfbplug1 6dum/ g a.z: (l.ront) 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 poe w4q v(1m;xof 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 highway nigdc yr n5k+/3+ish2.we 9jkat 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 2.3at4 q tgip+,;h0$ \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 eanp7bxyh ak, t4z;0(uz/ rku y1ch other head-on. Each has a speed of and they spot each other when they are initially 11.0 km apart. How much t 0a ; xhtur4ky/,1n(pkb yzz7uime do the pilots have to take evasive action?    s

  An airplane is heading due south at a speed of 60xnfo+:9;jeuv9o akdcf udgu4:h 9w5 ;0$ \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 in t nco-hc9sm6kf x( g sq, :mlg/bv;v47Problem 41 so that it will fly due south? bm6,g(:4tm9v clc-/7h nxk vss;gqfo   $^{\circ} $ east of south

  Determine the speed of the boat with respect to,,oh+jr5eh8p h 4lee qkx29l c the shore in Example 3–11.   

  A passenger on a boat mok5ldz exi: i00ving 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 i10uf768i j3ofswm 7vid7ap(bu.gh ytn still water is 2.60 $\mathrm{~m} / \mathrm{s}$ must aim upstream at an angle of 28.5$^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current?   
(b) What is the resultant speed of the boat with respect to the shore?   

  A boat, whose speed irks* h/n13n/vr8 pnoyn still 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 ofaf/ jon* ,8 hd* zw*5iwsu5prb 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 0.45rwe p9z2er85 t $\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 speedxr:r/lg x-40mc::fsf:n9wnp6 wv jh l is 620$ \mathrm{~km} / \mathrm{h}$ is supposed to fly in a straight path 35.0$^{\circ}$ north of east. But a steady 95$ \mathrm{~km} / \mathrm{h} $ wind is blowing from the north. In what direction should the plane head?    $^{\circ} $ north of east

  An unmarked police car, traveling a cons(9jf6) e ng xor3mgh9ytant 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 speedeygl 2-qm:xu/vxqnb-bl( qw 4wf(l3v, r’s speed is not known. If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what ,( bvm4w nq-v2-g wxlf/ buy(x:3 lqqlwas the speeder’s speed?    km/h

  Two cars approach a street corner at right a 252w;cvx rrxqngles to each other (Fig. below). Car 1 t;v2cx r5qrw2x ravels at a speed relative to Earth $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , and car 2 at $v_{2 \mathrm{E}}=55 \mathrm{~km} / \mathrm{h}$ . What is the relative velocity of car 1 as seen by car 2 ?    km/h    $\theta$$^{\circ} $ West of North
What is the velocity of car 2 relative to car 1 ?    km/h    $\theta$ $^{\circ} $ south of east

  William Tell must split the apple at u6uzik*to /ch/)d,c*s*n gu bop his son's head from a distance of 27 m . When William aims directly at thkd g*tuuz,csb* i/ )no6 /cu*he apple, the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck214nhdf;dl. wv7 sid n, 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 horizonn h.l7s fi21v;d4ddwntal planes. Assume x is east, y is north, and z is up.

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

  On mountainous downhill roads, escape routes are sos0glc na1d4km/8xl v g2royu )t(l+,pmetimes placed to the side of thox/4 vgau20p sgt r1dl+8lcn) l(, kyme road for trucks whose brakes might fail. Assuming a constant upward slope of 32$^{\circ}$ , calculate the horizontal and vertical components of the acceleration of a truck that slowed from 120 $\mathrm{~km} / \mathrm{h}$ to rest in 6.0 s . See Fig. below

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

  What is the y component of a7 v0ztn2zh,57u vxrto vector (in the x y plane) whose magnitude is 88.5 and whose x0tt7v2z,ouv 5hx 7zrn 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 angl3 p +rv5v8hgk. 1kzmi)n4oqiye $\theta=30^{\circ}$ with the vertical when viewed through a moving train window (Fig. below). If the speed of the train is $20 \; m/s$ (a) what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically?    $m/s$
(b) what is the speed of the raindrops relative to the train?    $m/s$

  A light plane is headed due south with a speed opyzv j6 j4 tdoz4ve,k;b1i7e+f 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 ej76qc,lnxmaa 2coex 0t: 9(i $\mathrm{~km} / \mathrm{h}$ 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 8.0 m .l 9k:rck p2n68v n-sra Assuming his horizontal spekks8 p6:aln-nv r2cr 9ed is 9.1 $\mathrm{~m} / \mathrm{s} $ as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright - that is, the same way he left the ground. t =    y =   

  Apollo astronauts took a “nine iron” to the Moon and hitp z zlf.67;hja 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 resistanc76fj zazl.p h;e in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a hoh8gjtr f ig e.oet+-89mer 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 Afsytvz fd rq/5 9k0u.+capulco push off horizontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water level thar dk./t5q9+f zvfuy0st 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.a7 ;100, c wwtbcwkzaf What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the serw7w00,fcb a k1z;cawt ver 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, flyino6 jk1rb.p c+ng a constant $215 \mathrm{~km} / \mathrm{h}$ horizontally in a low-flying helicopter, wants to drop secret documents into his contact's open car which is traveling 155$ \mathrm{~km} / \mathrm{h}$ on a level highway 78.0 m below. At what angle (to the horizontal) should the car be in his sights when the packet is released (Fig. below) ?



$\theta=\approx $   $^{\circ}$

The speed of a boat in still water is v . Thy b7:;gax +jjmfci 2+me 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 b +m ;7jjxm:aiyg fb2c+oat 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 oyw44m - e4g5n8gilela cliff which is 195 m wi 4n4 y8 gme-olg45elaway and 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 qj ara3yk ,qt7z)kojr0tq c9ex43irbn87u): at a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The player likes to shoot the ball q)uxz:79i8r3 4j)0cj rqar kqk3te7a ,ntobyat 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 q6i,a diyyose77;( jo0 ienx4 of a $5.0-\mathrm{m}$ -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 u ya,l +ekz mb:jc59frsz28/uto make his car jump over eight cars parked side by side below a horizontal racublafr/:59u m2es8 ,zzyk+ jmp

(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 6bh,n.z7t9;nx. a n0mpazt2mftsku 3 0.90 m above the ground at an angle of a ba z,;0 .mnmsht63ttz 7fnnp9x.uk2 $61^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s} $ heading toward centerfield. Ignore air resistance.
(a) How far from home plate would the ball land if not caught?   
(b) The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level.

Find his speed.   

  At t=0 a batter hits a baseball with an j :t 3drptz(5;bj+aomv5 idn 87;iovoinitial 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 =    $^{\circ}$

  A ball is shot from the top of a buildionra)s pbrz; 4ru;y 6mm a6;,jng with an initial velocity of 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart gun, and being a clever physd3 ob0lb10h arics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.0 s for the dart to land back at the blo0 arb1hdb30arrel. What is the maximum horizontal range of your gun?