One car travels due ecvj4rjr5d2hp wa7lxzi4 mny :86 sl7)ast at and a second car travels north at Are their velocities equal? Explana:hv4rxd jw7 l)mrz 728 cy4slp 56jiin.

Can you give several 8pu rp hr-4+kqexamples of an object’s motion in which a great distance is traveled buhqurp 4+ 8k-rpt the displacement is zero?

Can the displacement vector for a particle moving in two dimensions ever bxxtru5mzki*m,0nru (8b 5s)ae longer than the length of path traveled by the particle over the same time interval? Can it evsx 0rum,*im5 uxk bat 8nr5)(zer 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 leng/w:1u7 ych qqtth $ 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 a3ink ucvh zlfg; g(-28dd up to give the zero vector? Can three unequal vectors? Undch-kviz g;nu(28gfl 3 er what conditions?

Can the magnitude of4jt0y adh*p3y a vector ever (a) be equal to one of its components, or (b) bdyhpa 4*t y03je 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 0dke- hh1ug-fget on a moving “car” the riders first hop onto a moving walkway and then onto the cars - fkeuh-1d 0hgthemselves. Why is this done?

If you are riding on a train thate50 -3y3 rjwf; tsxspw speeds past another train moving in the same direction on an adjacent track, it appears that the other train e3-fstr jw3p s;y0x5wis moving backward. Why?

If you stand motionless under an umbrella in a rah8rz(:st8 8vpo w(qm3 lu/pdginstorm where the drops fall vertically, you remain relatively dry. p ow8 zpm8:8v(ur3/gt(hs dqlHowever, 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 velocity, throwdc6*yj y9k* ans a ball straight up into the air in her refen9kd *a6 yjyc*rence 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 jb-*jjw;yw,i h5d) knrow at the same speed in still water, set off across a river at the same time. A heads straight across and is pulled downstream somewhat by the current. The B heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reachjwj, *)-bh jwkiny5;d es the opposite side first? ----待选择----AB 

How do you think a baseball player “judges” the flight of a fly 7t;8hs*z)q; j 6mr8ux*gr*gakh wj e vball? Which equation in this Chapter becomes part of the a j ;7)qk**jr6sew8zugghm*vxr;8 htplayer’s intuition?

In archery, should thhuem;q7w6fx*g 7s1 qze arrow be aimed directly at the target? How should your angle of aim depend on the distance mfush7w;*xg q1eq6 7zto the target?

  A projectile is launched at an a /d)ngw;d9rg gngle 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 with identicawu 3pk7 z)uekz5:8pitl initial speeds, buik 3w tzp: pe8u7z)k5ut 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 displar7ep.: j ut5dxcement of the car from the point of origin (magnitude and 5:u.j rdetpx7direction)? Draw a diagram.

  A delivery truck travels ukc5un 2zym/*o js 58u18 blocks north, 10 blocks east, and 16 blocks south. What is its final displacement from the ori/s ozuyu55k j2mu 8c*ngin? Assume the blocks 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 determinesx gx;kk+ 4 rbxhc;0dz lh8-k; the resultant of the following three vector displacements: (08-gbslr+ ;hx hkkkxcz x;4 ;d1) $ 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 ve 2.6fys5 e k*l)tsgd*4b irehkctor $\overrightarrow{\mathbf{V}}$ 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 travelib1 g b8dv-wmw(,7pg kyng $735 \mathrm{~km} / \mathrm{h}$ 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 Fig. below. Their magnitudes are given in arbitrary uv0-z)w nk(q1:jv/ tiofvo8c c nits. Determine the sum of the three vejko:0 cov-(wq1 vnz8c/ tivf) ctors. 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 vector u,ga +ru9nb*ps $ \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 campl:ze )webl;,v, is measured on a map to be 4580 m horizontally froleweb:l ; ),vzm the camp in a direction $32.5^{\circ}$ west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north, and z axis up. x =    y =    $|\overrightarrow{\mathbf{r}}|$ =   

  You are given a vector in the xy plane that has a magnitude of 70.0 units anhj:h1/p ass *4w de),mb zi3and a y component of What are the two possibilities for its x cosa hn4mhp3z1 d/*aebjis:) w,mponent? x = $\pm$   

  A tiger leaps horizontally from a 6.5-mdtxz. 3roar lp*e+-+y 32n r6n 3jgmt9enco)s-high rock with a speed of How far from the base of the rock wi++)g3*ld oact9ne -n.ry3 jm 6nret rzx3po s2ll she land?    m

  A diver running dives out horizontally fr2zdvcbmffbfxr 6f4 1 ,/,uh n1om the edge of a vertical cliff and 3.0 s later reac6ub1,fcd / 2vxhrf4bf z1,nmf hes the water below. How high was the cliff, and how far from its base did the diver hit the water? high of cliff is    the distance is   

A fire hose held near the ground shoots wat wy5z aks1 ()f)y5ccgger at a speed of At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. below)? Why are there two different angles? Sketch the two trc g5s)(1g5 zac)kwfyyajectories.

  Romeo is chucking pebbles gently up to Juliet’s window, and he w :z v,2f2ye leh,d)tarants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. below). How fast are the pebbles going when they hit her windowt2 rd ,)2z e,yefalh:v?    m/s

  A ball is thrown horizontally from the roof of a building 45.keor xsj;47v g l7+tos18h3 jczj-dh80 m tall and lands 24.0 m from the base. What wasz7; odtxjs-l3o7+1jk8he 4rc hvgj8s the ball’s initial speed?   

  A football is kicked at ground level wi)0ydg)g3id h;/jiw pte32di2:m susoth 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 buildutnk xb;.)hn 5ing lands 36.0 m from the base of the building. Hx5n) kn.u tbh;ow tall is the building?    m

  An athlete executing a long ju25wvwu )c u+olmp leaves the ground at a 28.0$^{\circ}$ angle and travels 7.80 m .
(a) What was the takeoff speed?   
(b) If this speed were increased by just 5.0 % , how much longer would the jump be?   

  Determine how much farther a p3 gsxdh. j(1wierson can jump on the Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moon is jd.iwx(g1h3 sone-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) 75.0 m ax 9ma 81afua*kway.
(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 travetk2 wdi6 m/-gs: y)m2qen;whqling wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropp;tdqm:)e yh kqig 2s2/6-wmnwed how many seconds before the plane is directly overhead?    s

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

  A projectile is fired with an initial speed of at an angle of 34*slit3ioenf07n78 + ypot:j e3g bso 8.5$^{\circ}$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot from the edge of a cliff 125 is9*a9c jcg;7s2tq wv f8l1iam above ground level with an initial speef w qic ac8vt*1;sagsi9j279l d of at an angle of 37.0º with the 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 shotl 4webg+d./ec with an initial speed of 15.5 $\mathrm{~m} / \mathrm{s} $ at a $ 34.0^{\circ}$ angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 m above the ground.   

  At what projection angle will the range of a prm3u y;lghg5-:5hw -ug7wyttnxx;zo 1ojectile equal its maximum height? wy1;t35gxz-g uwo t7- mgl x;:hyh 5un   ${\circ}$

Revisit Conceptual Example 3-7, and +2aqo5um s a7qhii7s56gpi)j assume that the boy 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 lettinghm6j poa5s+5 7s qiqu)i7gia2 go at the moment the water balloon is shot.

  A rescue plane wants to drop e(0+ vk e sw*.bzsmi0ksupplies to isolated mountain climbers on a rocky ridge 235 m below. If the plansk ek+b0zw(.s *m0ive e is traveling horizontally with a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

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

  A person going for a morning jog on the deck of a cruise s 2op iq2,rlvavh0*oncm-n dn8* n f1k;hip is running toward the bow (frk-2nnc 8n,o*v q*02nm vh1lo;fpdiar ont) 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 spee /)u;vpeall;3m fxe,ed of 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 sout:v wn*ndj,wtorpz:- 8q ay* g;h on a highway 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.k. sts(5 ciw5w30$ \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 hetw61bp)a8bkl ad-on. Each has a speed of and they spot each other when they are initially 11.0 km apart. How much time do the pilwatbb6 1l8 kp)ots have to take evasive action?    s

  An airplane is heading due south at 6egpzeo. 38ac uuq-f-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 trr0l 0p zr5g.s)m sx+ghe pilot aim the plane in Problem 41 so that it will fl. zx 0rgs5gps0r)ml+ry due south?    $^{\circ} $ east of south

  Determine the speed of the boat withbq ng6h5n 44oq respect to the shore in Example 3–11.   

  A passenger on a boat moving at 1.5hhuol-xk bkhc(l a3)zw31x0 ,0$ \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 cri803l dsw3cfhu mpn)0x ;l-za*i -ustill water is 2.60 $\mathrm{~m} / \mathrm{s}$ must aim upstream at an angle of 28.5$^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current?   
(b) What is the resultant speed of the boat with respect to the shore?   

  A boat, whose speed in still water is vzx+:e+t ;ux u2kfq 1tz3jw6e 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 ord5f+bqy5 cs2l ;, ( gbq-tawof 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 swimmib vglc6* w/m-4isacq(1j: ky yng 0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?    $^{\circ} $
(b) How long will it take her to reach the other side?   

  An airplane whose air sq5 znynwq5;:ppeed 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, .s t7s1 tpvzujjklvc70)5)o htraveling a constant 95$ \mathrm{~km} / \mathrm{h}$ , is passed by a speeder traveling 145$ \mathrm{~km} / \mathrm{h}$ .

Precisely 1.00 s after the speeder passes, the policeman steps on the accelerator. If the police car's acceleration is 2.00 $\mathrm{~m} / \mathrm{s}^{2}$, how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)?   

  Assume in Problem 50 that the speeder’s speed is not known. If the:4 6 pi+ifiu u64-9hgjxzyqb v/a8xfa police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was the spu a964av/x+gi p 846:f-ufyxzjqh iib eeder’s speed?    km/h

  Two cars approach a street corner at right angles to each ot0(vsgy9, t s :2ao98mh0kqhxhvxz gx/her (Fig. below). Car 1 travels at a speed relative to Earthk/g9xo8 sa v,gxhsqh0tv0: xzm ( yh29 $v_{1 \mathrm{E}}=35 \mathrm{~km} / \mathrm{h}$ , 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 pnlb/ n9 c kg+ **-mwex.38 k/cgmdacfa distance of 27 m . When William aims directly at the apple .lc/ /fmcem+k*3d gg8nwxca*- npk9b, 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 truck, walks 50 m east and 25 m south, and then takez+m7k y5zhe8e qzv b nx9aqp;1,(k3uts an elevator 10 m down into the basement of a building where a bad leak is occurring. Whae yzz5(ktqbq3p7x,9zm1k;8u v e a +hnt 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, escaau2 l92z)2yu.s7e zx v1jzsgx pe routes are sometimes placed to the side of the road for trucks whose brakes might fail. Assuming a constant upward slopex7 9u 2jvgz)laz 2.2xyeus1sz 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 rn 1pkmrs 25px *bvw/*ja7zm)vector (in the x y plane) whose magnitude is 88.5 and whose x component ia7*2 npp5rwm r jsxkv*b)m 1/zs
75.4? What is the direction of this vector (angle it makes with the x axis)?
$\text { Direction }$=    $^{\circ}$$ \text { relative to } x \text { axis }$

  Raindrops make an angle sjf 1k1viye)x-+d*m) j*a3 p 6rbuuzj $\theta=30^{\circ}$ 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 car0e9l-ubh51b idb4 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 ()xpfelc i*8z$\mathrm{~km} / \mathrm{h}$ 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 . Assumingeqflxo a u( e.1t-5m9j his horizontal speed islxfq9(- .atju oeem51 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 to6 4c:yxp (dfq5 (yuuuaok 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 surfaa :p4uu5qy (dx6ucyf (ce of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer h;6hqt0(dck msr r6lqlg2 k*(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 Acapu8)qv1h syb0cyt k6/q flco push off horizontally from rock platforms about 35 m above the w1vf yqq/0 )tys 86bhkcater, but they must clear rocky outcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. below. What minimum pushoff speed is necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis playe g2*y8 9z qvw::nmxnplo:x c4ar aims 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 “8lnazx:n94 y g :cvp*2 xomqw: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 ax 2*w 1rtlwdl* 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 boat is to makexj8 ;y;(n+)fsk3sw p an,j wqr a round trip in a river whose current travels at speed u . Derive a xwns(as+8)jwk fpnq3 ;yj ;,rformula 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 across the river and back. We must assume u

  A projectile is launched from groun5ju +7kz j(sznd level to the top of a cliff which is 195 m a 7zk j+sjunz(5way 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 at a height of 2.10 m aboveusxtx 8l- +m2k oqfl.. the floor. The basket is 2.60 m ab.2mlos lkx- fxqu+8.tove the floor. The player likes to shoot the ball at a 38.0$^{\circ}$ angle. If the shot is made from a horizontal distance of 11.00 m and must be accurate to $\pm 0.22 \mathrm{~m}$ (horizontally), what is the range of initial speeds allowed to make the basket?      

  A high diver leaves d/79c/bfpe ymz6rz nx ku::4sthe end 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 to make his car jump over eight cars parkean*t8 ,r 3* nyrnurm7td side by side below a h r rumnratnyn83*7*t,orizontal 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 anyb6 7sf3/dnt8u*pj u(p/qs ur i -hn7bgle of 36usy hnus /b j*t rp(-u78nid7q/fpb $61^{\circ}$ 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 initial speed ox+ncn rs jsv24m7d ;h(f $32 \mathrm{~m} / \mathrm{s}$ 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 building with an initial velocity of ,5)wkk v:kp rd18$ \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 physnr p-,ozb i ;j)4ajc/fics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4;boj4 nz,pfaji )c/-r.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?