One car travels due east at and a second car travels north at Are the /1+g j ekufz6p:(kcbair velocities equal? Explap +f:1a6k(zkeugjc /bin.

Can you give several examples of an object’s mok3uw6 lk3z+jy tion in which a great distance is traveled b+j3yu 6k3wklzut the displacement is zero?

Can the displacement vector yu4/t+krkieb1x l-5jfor a particle moving in two dimensions ever be longer than the lengt 5et-yi4kxrju1b k l/+h of path 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 length us(mv8 ;tc k0n$ V_{1}=3.5 \mathrm{~km} $ and $ V_{2}=4.0 \mathrm{~km}$ . What are the maximum and minimum magnitudes of their vector sum?max =    min =   

Can two vectors of unequal magnitude add up to give the v0tdpp5oh - a.z9q)cu zero vector? Can three unequal vectors? Under what conditi5 utv .-09)aodpzc phqons?

Can the magnitude of a vectou:p -7ini .dgo+ymxa fl(j,o *r ever (a) be equal to one of its components, or (b) be less than one of its compi7a x -jo.yd pm (oifgl*u,n:+onents?

  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 fi 9 qtv0bufq4b+rst hop onto a moving walkway and then onto the cars themselvesbq0q4 bv9+fut. Why is this done?

If you are riding on a trainfm3mlr )8xhe*m:p s s/qtbh2 3eg; 8lo that speeds past another train moving in the same direction on an adjacent track, it appears that the other train is moving backbm emh23hs f* e8xr qltm:lo)p3 ;s8/gward. Why?

If you stand motionless under an umbrella in a rainstowb(fwm24op*t 5* u*ddpr: a) 7k tyeycrm where the drops fall vertically, you remain relatively dry. However, if you start running, the rain begins to hit your legs even if they remain un y c**y(frd p4 w 2p:wu5oet7kdbtm*)ader the umbrella. Why?

  A person sitting in an endtoy12:g+vb 5ucv x/vclosed train car, moving at constant velocity, throws a ball straight up into the air in he2/ otv1v:b y+gu 5xvcdr reference frame.
(a) Where does the ball land? What is your answer if the car  ----待选择----ahead of herbehind herin her handsher left 
(b) accelerates,  ----待选择----ahead of herbehind herin her handsher left 
(c) decelerates,  ----待选择----ahead of herbehind herin her handsher left 
(d) rounds a curve,  ----待选择----ahead of herbehind herin her handsher left 
(e) moves with constant velocity but is open to the air?  ----待选择----ahead of herbehind herin her handsher left 

  A and B rowers, who can row at the same speed in +pb fi0 /5fyxcstill water, set off across a river at the same time. A heads straight across and isyfc0 5 fbp+xi/ 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 opposite side first? ----待选择----AB 

How do you think a baseball player “judges” the f*h *vo 5 5uctlacrlyq zo33amw/(e.w4light of a fly ball? Which equation in this Chapter becomes part oflvqaw3e o ra ./*yuc35mth 4l5(ocz* w the player’s intuition?

In archery, should the arrow be aimed directly at the target? How should your an*iet- w(4pydrpxi4c w8v.hl8 gle of aim depend on the distanv pcehwp -wi x8l(.dt* yi44r8ce to the target?

  A projectile is launched vw:g qu/h)/gpat an 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 fromr,cq2 qcptcgq dpgys 167.-r nj ,/)bk the ground with identical initial speeds, but with b71r gt/gkn.6cr,pj2c, p-qqdq) scy $ \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 the8crj w(w7pms:l5rj 2an 85 km southwest. What is the displacement of the car from the point of origin (magnitude and directi 8p:5l rjrc7 m2(awwjson)? Draw a diagram.

  A delivery truck travels 18 blocks north, 10 blocks0 phmpat88h 3kk bmj)/;s yat/ east, and 16 blocks south. What is itsbk0; mamaj )/htt8 /psy3 hk8p final displacement from the origin? 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 determine the resultant of the following three vector displacemen+ /w8j5/ t .e5idpe0ieca uctf/zuf,k ts: (1,a/c0i edfeui .ctp5 wk/8f/+tejuz 5) $ 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 vecaru-q t4ln0b -xn6 58sq 6xomntor $\overrightarrow{\mathbf{V}}$ 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 s7:- g t2kdo j:nqcifqq o7bwv,wb3.) $735 \mathrm{~km} / \mathrm{h}$ 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. .8p 8:sxjpx c/hc+ledTheir magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in h/lcx cp+.8sj 8:d epxterms 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 ar (b/z,m8cqf $ \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. s/r-;zo yk ,1f(3bhnztltll , 2450 m above base camp, is measured on a map to be 4580 m horizontally from the camp in anz tolkf1ht 3l.; -b/lzr( s,y 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 plaepe+znaa . z )6s 2gxkgfwj(6/ne that has a magnitude of 70.0 units and a y +e/ .s(k66 zpa)nw2jgzfegax component of What are the two possibilities for its x component? x = $\pm$   

  A tiger leaps horizontally from a 6.5-m-high rock with a speed of Hobf-3mxo5zl; j w far from the base of the rock will she land? lb 5 ;oxfz3-jm   m

  A diver running dives out horizontally from the edge of a verti0wty/8yd au.lf()tfw zon*cv6 8 i ta6cal cliff and 3.0 s later reaches the water below. How high was the cliff, and t 8 t8acfav0nwluy*6zw ()o y6.d/ifthow 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 water zxl73,k-2n 6dpc snj * (izzfwat 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 differenn3( ks*n 2w- ,jizdfz7 plzc6xt angles? Sketch the two trajectories.

  Romeo is chucking pebbles gently up ;e0j c*x hg /zx,sno:mto Juliet’s window, and he wants 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 herxn zscjoe,m:*h/ gx ;0 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 buildr jg5los 355gr7vm2szing 45.0 m tall and lands 24.0 m from the base. What was the bg5o zrrs2 3 g5mvj57slall’s initial speed?   

  A football is kicked at gr-:ogje + )u9 aggfeb/kound level with a speed of 18.0 $\mathrm{~m} / \mathrm{s} $ at an angle of 35.0$^{\circ}$ to the horizontal. How much later does it hit the ground?    s

  A ball thrown horizontally at fr av*)2egi m6riom the roof of a building lands 36.0 m from the b6marvi)g* 2ei ase of the building. How tall is the building?    m

  An athlete executing ,wx,8 nhkut4piclu04 5x d uss-v:/nm a long jump 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 person can jump on the Moon as compared to thei:y+c4 nyst :e 6mm), gbkksl ;le3-db Earth if the takeoff speed and angle are tsg 3tdnbsm4cmkl+ k i);,y ylb ::6ee-he same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.    times

  A hunter aims directly at a target (on the same level) r6 vxvpnvt;i n 8(yk+w+6l8rx75.0 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 travel5 pscv: njj6l32 zv yjw:ynq3l0h( 3awing wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how 3:v z06: v3cyj5waq 2yl3pn jl(nhjs wmany 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 ;wy,8iyxxu6 q.0xjqxnx4smt6nuc/- with an initial speed of at an angle of 34.5$^{\circ}$ above the horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile,    m
(b) the total time in the air,    s
(c) the total horizontal distance covered (that is, the range), and    m
(d) the velocity of the projectile 1.50 s after firing.    m/s

  A projectile is shot from the edge of a cliff 125 m above ground levgu;t lo9.v6a xel with an initial speed of at an angle of 37.0º with the horizontal, as shown in Fgx6au; v o9.ltig. 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 initih ):ts2e/vt x wmjnk--al 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 th)y7 3j3dtbj ibe range of a projectile equal its maximum heighttbibj jd)y7 33?    ${\circ}$

Revisit Conceptual Example 3-7, and assume that the boy with theund45b 8v q**9pazg + 6txztug 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 balloon is shot qatuunz65+ *4t8 pb*g9gzxdv.

  A rescue plane wants to drop supplies to isolated mountain climbers on zcjx1x( b l-b)h/ wt-r4 ) v8ojxbzul4a rocky ridge 235 m below. If ljc)-zx84xb -lzbovwuj()/ tx 1h rb4 the plane is traveling horizontally with a speed of 250 $\mathrm{~km} / \mathrm{h}(69.4 \mathrm{~m} / \mathrm{s})$

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

  A person going for a morning jog on the deck of a c:lhnn(f .c +a8ndla,enxcbvp)g ; 8g9ruise ship is running toward the bow (front) gdn8ennaa+ll9p 8,( v.cgnc hxbf: ;) 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 s5jq +x*7hf te;4c pzd 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 ;1ms dh tv5srqwl (8/fon 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 2.30yu11 rpja(fml x(9q w3$ \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 head-on. Each has a speed of and they spotjs7d cjy1 4cq1a . 3be1ujfecg,9p a6x each other when they are initially 11.0 km apart. How much time do the pilots have to take9x1 4jdua,7 611g.jb qycejscp fa ec3 evasive action?    s

  An airplane is heading due south at a spee67geysjq.tt z1fnt-6 b ao6 ;an(sa3xd of 600$ \mathrm{~km} / \mathrm{h} $. If a wind begins blowing from the southwest at a speed of 100 $\mathrm{~km} / \mathrm{h}$ (average), calculate:
(a) the velocity (magnitude and direction) of the plane relative to the ground, and    $^{\circ} $ east of south
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.   
[Hint: First draw a diagram.]

  In what direction should the pilot aim the plane in Problem 41;snh6nw:l6 ah so that it will fly due souh:;h 6n6nalwsth?    $^{\circ} $ east of south

  Determine the speed of the boat with respect to the sho iib.-ikjui9bg q ,,:8hj k1mire in Example 3–11.   

  A passenger on a boat moving at 1.j6 ki;2)gmy zv 3vmj4v50$ \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 wabu s4/. ynlj2z ,r f;enqr;5veter 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 stib.ogk c31 ia;f+bl5jt ll 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+1u bt .tv(o12ut:zv 8jwpsbcdpg, ;x 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 nk s( mfm:6,le0.45 $\mathrm{~m} / \mathrm{s} $ in still water. (a) If she aims her body directly across a 75 -
m -wide river whose current is 0.40 $\mathrm{~m} / \mathrm{s}$ , how far downstream (from a point opposite her starting point)
will she land?    $^{\circ} $
(b) How long will it take her to reach the other side?   

  An airplane whose air speed is 4 m83f p59i 5lcl)ow:frhji ap3+gpub 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 constant 95lcz9hr-- bem*ipx, mk/u87x l$ \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 speederv0d.)qkt8 p pe’s speed is not known. If the police car accelerates uniformly as given above, and overtakes the speeder after 7.00 s, what was the speede )0.pvt8 kqepdr’s speed?    km/h

  Two cars approach a street corner a 2rbwky0zw1:g;3 1qpz2 tauyft right angles to each other (Fig. below). Car 1 travels at a spww r2kfzyu;b21a3py0 1 : tzqgeed 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 fp k/nq,(7yda5e qqrf0v6p j/his son's head from a distance of 27 m . When William aims directly at the apple, the arrow is horizontal. At what angle must he aim it to qvp/k7fj a f q(0eyn/rp6,d5q 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 h-1hm9f:i h iwm east and 25 m south, and then takes an elevator 10 m down into the basement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components, and also give the magnitude and angles with the x axis in the vertical and horizontal planeshmfi19: - hihw. 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 sometimes placed to thiuqpq ab 4d6(9e side of the road for trucks whose brakes might fail. Assuming a condpq9qb 46u(i astant 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 magnitud fp(wtp.lq1,z xh 8/uoe is 88.5zp xh1(pow qt.l,u/8f and whose 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 angle7pkx of,k*xgen)td 9- $\theta=30^{\circ}$ 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 of ohkprtxcu 33u8ho9*zz 5t3 s: 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 .o8*wyjyaq9. okbqav4 d2 a0- vao4an$\mathrm{~km} / \mathrm{h}$ 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 . Assuming his hlgz+t5a h; hup b7hy27orizontal speed isag b7t; puyhz2+hl57 h 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 a77 nb+ ( li/qno7o:br8gqofo k u2zb.q “nine iron” to the Moon and hit a golf ball about 180 m! Assuming that the swing, launch angle, and so on, wer: 7k.olqqnbbof +uzo no/b2r i(787qge the same as on Earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!) g$_{moon}$  

  When Babe Ruth hit a homer over the 7.58uh1z4 rcerm e 4wegu: (ytl75$-\mathrm{m}$ -high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat?    Assume the ball was hit 1.0 m above the ground and its path initially made a 38$^{\circ}$ angle with the ground.

  The cliff divers of Acapulco push off horizontally from rock)k rwt 1fq0d+b platforms about 35 m above the water, but they must clear rocky outcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. below. What minimum pushoff speed ikdt)fq+ b1wr 0s necessary to clear the rocks?    How long are they in the air?   

  At serve, a tennis player aims to hit the ball horizontally. Wh2lj6q1jpt*lz.y dn 7nat minimum speed is required for the ball to clear the 0.90-m-high net abouz t7 1yjjnd6pql.*n 2lt 15.0 m from the server if the ball is “launched” from a height of 2.50 m? $\approx$    Where will the ball land if it just clears the net (and will it be “good” in the sense that it lands within 7.0 m of the net)? How long will it be in the air? $\approx$    See Fig. below.

  Spymaster Paul, flying a con.e0tu c0bxtt 2stant $215 \mathrm{~km} / \mathrm{h}$ 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 wateb 30)tuqti k2fr is v . The boat is to make a round trip in a river whose current travels at speeut)tqi0kb 3f2 d 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 across the river and back. We must assume u

  A projectile is launched from gro u 3 vuz.nx2il,,s(myzund level to the top of a cliff which is 195 m away and 155 m hig vzs2muu (x.3 lin,y,zh (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 absbe6j xdtptu+m)iq.: ( glx.(-vu 7jzove the floor. The basket is 2.60 m above :dujg+bx6 jem s-(ivl t(7z )t.xq.pu 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 the end ofks,z jfl;+o1ofxg0j0v -t 9hv cd9l/r 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 parked side by side brrt g.q:ad -a4elow a horizontala:4rdg.r qta- 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 baqzyuy05q/ 0z 0ql so/e8fib-ct 0.90 m above the ground at an angle ofqouy5qsi0q /eybz-f /0 0cl 8z $61^{\circ}$ 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 annk;pqr+ 0 yvc/g6sal/ 3f tvc8/4sdwh 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 top of a building with an d c3+*pbrx/ibinitial 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 clevebp *jd008zp* syuzu1, h.r j2wm*wnrkr physics student you decide to do a quick calculation to find its maximum horizo*ywdk 2jw1h0us0* rju8bmpz *r, z.npntal 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 horizontal range of your gun?