One car travels due east at and a second car tramk7 ti*f(n(n.7 bf zccvels north at Are their velocities.t( (7kcz * cnfmf7nib equal? Explain.

Can you give several examples of an object’s motion in which a great distan9 7mx:5 lnbyfnce is traveleb95 nynfxlm7:d but the displacement is zero?

Can the displacement vector for a particle moving in two dimennq 5kw/ 6bz7sga8o 7aqsions ever be longer than the length of path traveled by the particle ovewgb7qzao75a/6qn ks8 r 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 len jw;ym3n 3rzd1p(l1q i,we c4xgth $ 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 magn 2q)rjhd:m,s: 7eeang itude add up to give the zero vector? Can three unequal vectors? Un:n7hms:dg2qa )rje ,eder what conditions?

Can the magnitude of a vector8 xhu/ ,vrm2 runxji(3 ever (a) be equal to one of its components, or (b) mrr x,xu3n(ji h/8v2ube less than one of its components?

  Can a particle with constant speed be accelerating? ----待选择----YesNo  What if it has constant velocity? ----待选择----YesNo 

At some amusement parks, to get on a moving “car” the riders first hop u,9cq f sld16konto a moving walkway and then onto the cars themselves. Why is t, kdlfusc9q61 his done?

If you are riding on a train that speeds past anothedz2 kll-/vt 9lr train moving in the same direction on an adjacent track, it appears that the othkll9v/- l2zd ter train is moving backward. Why?

If you stand motionless under an umbrella in a rainstorm where thev;v-sy;nzz ,a )qny7k6o 9eks1 i;z pu drops fall vertically, you remain relatively dry. However, y;zso, s u)ek-7yqzp ;1a9 in vv;k6znif you start running, the rain begins to hit your legs even if they remain under the umbrella. Why?

  A person sitting in an encreyf0bi 9cmh +c b 4a//.jlbc3losed train car, moving at constant velocity, throws a ball straigh/0 i j+/ rcbbh9ec mlfaybc43.t 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 o+ zyle2vz*tt t(ptar8)tc;d+ g /+lmsame speed in still water, set off across a river at the same time. A heads straight across and is pulled downstream somewhat by the current. The B heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reaches the opprg z(;pc/mdtt z8+ lt ve*)+at l2+otyosite side first? ----待选择----AB 

How do you think a baseballv u4vpqx:hn reuo)hao1w/9 3 z1-:vim player “judges” the flight of a fly ball? Which equation in this Chap1rumvvh: vq/a3u zpe ho4w: oi)1nx-9ter becomes part of the player’s intuition?

In archery, should the arrow be aimed directly at the target? How sho;s93v/ki p 7e 8qoxczz cmiog84ed8x .uld your angle of aim depend on the distan3q 97 ig;kdxp8eoc4s88 vc exziz m/.oce to the target?

  A projectile is launched at an rcj-+1hub2mtv)6 zut 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 the ground wia**v2g5h,-dybbblb ;k vhn.s th identical initial speeds, b,l5 nbbgsva-**h2yk ;h. bvdbut 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 and then 85 km southwest. What is the mhr1r j :z0k 23m7eivn7u czn.displacement of the car from the point of origin (magnitude and direction)? Draw a diazu0him1r3j kn2.7e :z n7 rmcvgram.

  A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks.tc 4;3gue.7p9 boykuifixrcw n1pirp 8)x 6 : south. What is its final displacement from the origin? Assume the blocks are equal leng p;uwgr)6 .inxu. kpcp3 ibr4xi:t 7f81oy e9cth.    blocks

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

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

Graphically determine the resultant of the following three v 5*fy;ujplt qe:z )tu6po5 .mxl9oi-q ector displacements:p-z 6foeluqtj )t*;5y uimop:5.lx 9q (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 vem;7i,s), x4i/gp *wd1wjm bukg rwcu2ctor $\overrightarrow{\mathbf{V}}$ 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 traveling q(md 3bozch 1k,k d9g5$735 \mathrm{~km} / \mathrm{h}$ 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 o/rl:5 qhc x.bin Fig. below. Their magnitudes are given in arbitrary units. Determine the sum of tr/xq5hc:. lo bhe 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 vectoruf;t)vzm 3 y8qoij;d;3f ry: ys $ \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 d mrr.9pdfd9: m above base camp, is measured on a map to be 4580 m horizont99 rdmpdf.:d rally 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 66. cfo:u v:ricb/g nzthe xy plane that has a magnitude of 70.0 units and a y component of What are thn/ci:66obuv rfgz.: c e two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a speed of ph, y2 ,yb8ocvpd1ct7 How far from the base of the rock wil27h oc1, bc,y p8vtydpl she land?    m

  A diver running dives out horizontally from the edge of a vertical cliff and89+ikpeap6ro4 rlj*yu5 ix s 4 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? high of cliff ipl yr59rx+ii*44a8o uek 6jpss    the distance is   

A fire hose held near the ground shoots water at a speed ol uo2 3lm )9id8gs2knjf At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. di2o28uljlg9skmn3 ) below)? Why are there two different angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up to Juliet’s wi2.jl24t iaj4 e exhnq*ndow, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a r4ejtx 2a hqnij*.l24 eose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the pebbles going when they hit her window?    m/s

  A ball is thrown horizontally from the roof of a building 45.0 d 5*/ ijaka 4z d(auv;u:lobyi8zv .;im tall and lands 24.0 m from thd4v(:l ayi* bozkav./j ; dau8iu z5i;e base. What was the ball’s initial speed?   

  A football is kicked at ground level*1ft lppet .:lhp;(+-a w lpbc 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 c kb4p agbc)lv+3 ::kotd6(rf 36.0 m from the base of the building. How tall i:gf6c) d4b3ov+kc (t:laprkb s the building?    m

  An athlete executing a long jump leaves the ground atk :k4gc:rkt sfy1w1g/ 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 farthe qe0 9tsgwu)2w n8;mcgr a person can jump on the Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleratunwgg2ctq ;9s0 em) 8wion due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directl :n5at-o/klcp,8zq 2qmb k*jvy at 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 suppli.f7b,lr2gzbs 5 4kflqt 1as rr.c -r1mes to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhe gb-lr1cbr. q fsraft,5z47 k12s.rmlad?    s

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

  A projectile is fired with an initial speed of at an angle of 3 cr+2zz.b7cx0ym5mmz.wl d5 x4.5$^{\circ}$ 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 fy24qxj: dx 1fjrom the edge of a cliff 125 m above ground level with an initial speed of at an angle of 37.0º with the1jj y4xqd:2xf 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 h :o vv(xw0:z 2,6kh8cxctx oespeed 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 0t .wt spm 7 yg tf.7fev(og3 7rooh5vov;9g4wa projectile equal its maximum height?yfg p0 vw.e4797 t5hto3t ;ogo gmovwf7(svr .    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with tbrvlxi2 v)+z qxq;67ghe 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 ballx gxvi+v );lbrq26q7zoon is shot.

  A rescue plane wants to drop ix e jy:f1,js.ej 3gcaq.d+t2 supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling.aq,jegfj dj3t x:1+ciyes 2 . 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 joqkne sivu r2 8*8v)7rlg on the deck of a cruise ship is running toward the bow (fqr r) 2i8eu*v7sl kvn8ront) of the ship at 2.2 $\mathrm{~m} / \mathrm{s}$ while the ship is moving ahead at 7.5 $\mathrm{~m} / \mathrm{s}$ . What is the velocity of the jogger relative to the water?    m/s
Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?    m/s

  Huck Finn walks at a speed of 0.)bvzcf /s 8a7h60$ \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 25 qi0t-6q7 vn3cjjkizw *dy 2 b)$\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 2.308 kssepns3i+ dwmt1099, gxcs$ \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 yqchgnf.+:6f other head-on. Each has a speed of and they spot each other when they are initially.chng +ffy q6: 11.0 km apart. How much time do the pilots have to take evasive action?    s

  An airplane is heading due south at a speed of 600o 9gae8ssbnvp8rv( p),-3 vbz$ \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 sho2(2h )sqiruo9zwr r j;uld the pilot aim the plane in Problem 41 so that it will flru2 hwj;(9z osr)2riq y due south?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the sho w7fog38yns e+re in Example 3–11.   

  A passenger on a boat moving atbxg ofk, g5m;) 1.50$ \mathrm{~m} / \mathrm{s}$ on a still lake walks up a flight of stairs at a speed of 0.50 $\mathrm{~m} / \mathrm{s}$ (Fig. below). The stairs are angled at $45^{\circ}$ pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?   

  A motorboat whose speed in still water is 2.x*ts li g znlid.y)1t)e ) vy*3-1qltw60 $\mathrm{~m} / \mathrm{s}$ 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 mxaf:ryo-(o9hh rew43kr g 750 lcsh*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 of, t*47xsglny j 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 swimx ffdy1wfi; 4*ming 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 speew0bjjq4v j. 9fuv)w xz,2:ihg3 *wgax d 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 po8u.))1;9d otqry7 v ifpflfa 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 e(kl+9o- yh ; -xqqu8ltl x8ps3ga8biis not known. If the police car accelerates uniformly as given above, andx8ai+u s (kt3-9qh 8p;-glyolel x8bq 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 ot dh:u0m,3)zh6ounz9s h 81mra; lhlupher (Fig. below). Ca,phu3odlmmlz nah 0:u1;) rz8h6 sh9ur 1 travels 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 atop his son's head from a dist:v fj:8kslsuj . hj+t tjr87z,6+fh5er0qoi tance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travehr l 5:fj 8,e+zuvi s86r qtf.:7ojts0tj j+khls at a speed of 35$ \mathrm{~m} / \mathrm{s}$ ?    $^{\circ} $

  A plumber steps out of his truck, walks 50 m east and 25 779q 8squjvu hm south, and then takes an elevatouqs7v 7h98 uqjr 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planes. Assume x is east, y is north, and z is up.

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

  On mountainous downhill roads, escape routes ard,e3f smc sa0*e sometimes placed to the side of the road for trucks whose brakes might fail. Assuming a constant ad* 0ce3smf,s 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 mag h3(l sk/pugh5jnya 22nitude is 88.5 and wha3 /p2ny25hhsl (guk jose 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 angj;mfl gm (u gl)t 2d78x a+l/x9hklumrq71jw:le $\theta=30^{\circ}$ 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*el/ jq vbe719prse5l,et 5 wvp+8juc with 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 f6o/fpb9dcckk( ,g 5u $\mathrm{~km} / \mathrm{h}$ 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 jump vpuv,,k z 8fcplg)n7dcit2r t2,s5 *r:lb1xter is capable of jumping 8.0 m . Assuming his horizontal speed is 9 )nti,rr:5 zfg7u2lk tpv8c2db ,tsxl ,1 pv*c.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 “7g4 9hz,)t cv. w1rvy(7 s2jieuouyyy 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 both cases, 17 v wy eycri4yu( zyujho,.vs2g9t) 7but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over tor,5go kq/zkip-j g59he 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 pusd g wdd,owdyxuh/g00-p,k3, th off horizontally from rock platforms about 35 m above the water, but they must cleu0d , dh0d kgwdox/3 gptw-y,,ar 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 aimmqe:46 7vkmb ni( ez/3 jyk1,hgug-wjs to hit the ball horizontally. What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is “launched” from a hei:vymhun e q3j7,g/k( bwmj-zi4kg16eght 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, flyine2ybrp4r- zt.3klqnxlt a 6:1g a constant $215 \mathrm{~km} / \mathrm{h}$ horizontally in a low-flying helicopter, wants to drop secret documents into his contact's open car which is traveling 155$ \mathrm{~km} / \mathrm{h}$ on a level highway 78.0 m below. At what angle (to the horizontal) should the car be in his sights when the packet is released (Fig. below) ?



$\theta=\approx $   $^{\circ}$

The speed of a boat in still water is v . The b 2 t6v: nlkof9koof.*0f b)ygmoat 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 (a) upstream and back downstream, (b) directly *g:lf0v9 mob)tf kofk2.yn 6oacross the river and back. We must assume u

  A projectile is launched from ground level to o m+ 56h g2gaycjkne32the top of a cliff which is 195 m away andkyg32a+mcej gno2 6h 5 155 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 plam to/4,.wzennyer's hands at a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The pla, mten.owz/n4 yer 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 o8c8 ybam cx+ p, y1mzc6,rzo)ff 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 to m,l2uv:qasdv )m) i,.dp 5vrwe ake his car jump over eight cars parked side by side below vevai)usp:dl ,.5 2 )rdm,qwv a horizontal ramp

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

  A batter hits a fly ball which leaves the bat 0.90 m above the ground atj gubw oj7h73e)29ey5ct (8 agmize0 gw:4bn a an angle ofej3 ubzn7y7e(oi2ggh:tj) w 5m 9awb8c a40eg $61^{\circ}$ 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 b71 ws2mx j;pfbaseball with an initial speed of $32 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is 85 m from the batter at t=0 , and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder's line of sight to home plate. [Hint: the law of sines may help]


v =    $m/s$
angle =    $^{\circ}$

  A ball is shot from the t;(gp2 fr-ama afk:3m lf5qlx7op of a building with an initial velocity of 18$ \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal.
(a) What are the x and y components of the initial velocity? $v_x$ =    $v_y$ =   
(b) If a nearby building is the same height and 55 m away, how far below the top of the building will the ball strike the nearby building?   

  You buy a plastic dart gun, and being a clev2t,se) )aej9q nw m5wzer physics 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 barrel. What is the maximum horizontalj e9,)nwq 2)awmtz 5es range of your gun?