Which one of the following is an exka 2z. dck *qdz8) depvp+-3ocample of a vector quantity?

  Which of the following operatfpm.c za2arc(a k8ch0 i, uiein)7 ;h.ions will not change a vector?

  Which of the following isd5sf wvai91 q7 an accurate statement?

  The resultant of two vectors is the ;cw:jia4 u-g8 7um,e (wa gahqsmallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 hj+7 dl-oe1bim, respectively. When these two vo-edhi bjl 17+ectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are add+j 4 7hr-r+pdt(tjxo3 nizv n;ed. Which one of the following is a possible answer for 4j th rn3z ijxvt(7r+op-n+;dthe magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull ont1ilbu- etu 6bux(azwm rko(,87+8nz an object in directions that uunk8 x- blz6iwt e8m, zu(a(7r+1botare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectog7 onbm,-8 uger is

  Ignoring air resistance, the horizonta6 sci3hg i el5. s(evs+g0u,ftl component of a projectile's velocity

  A ball is thrown with a vel-rjoqu /3*ajlocity of 20 m/s at an angle of 60e above the horizontal. What is the horizont /u 3r*ja-qjloal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal component of a proj 25nuistba,s 8lq;6nkectile's acceleration5ks ;8ba,nqisn tlu 62

  A soccer ball is kicked with a velocity of 25 m/s at an an/c+ 5y1mze vne6ej/0kqo imw 2gle of $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vector of an object is directed anti-paral6zut bji-wv56lel to the velocity vectot 6uwi6vjz b-5r,

  If the acceleration of an object is alway)sfye3f+e8s cv 9bdi ,s directed perpendicular to its velocity,fc 8 s9dse vf3ebiy)+,

  At what angle should a water- uv gd cs:(1dh/hl+nu:gun be aimed in order for the water to land with the greatesth:uc1l d/ dv +h:g(usn horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizonl2.)jdjpes, etal, each with the sa.) esdpj,e2lj me speed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second time. If nv6zhz+sy6 j 61s4l 4l9xtuo ni:)aqfmo9 ca*the ball leaves your hand with twice the velocity it had on your first throw, itc nfh+m j)9xanos*944zu6syo it ql6l:v1 6a zs horizontal range R (compared to your first serve) would be

  A ball is thrown at an original bddgv v10i6h7m5-)*nndravn6 dlko- speed of 8.0 m/s at an angle of $35^{\circ}$ above the horizontal. What is the speed of the ball when it returns to the same horizontal level?

  When a football in a field goal attempt reaches its maximum height, hz7ak;3lcc p32j b0vwgow does its speed compare to its iwc jp;v2370l3gz abkc nitial speed?

  A stone is thrown horizontally from the top of a tower at the sa,xum g*4zya 2nme instant a ball is dropped vertically. Which object i42g uanx* mz,ys traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet isz apuf7 ffjxxyfe-36 x*p7f-bdo 8f9* dropped from the same height. Ignore air resistance. Compare the times of fall of the two bulleoe y8jffpfd7 7* *69x pafx-ubfz-fx3ts.

  A plane flying horizontally at axtsy6 1 g(k2oq7j,xeda 23kn b speed of 50.0 m/s and at an elevation of 160 m drops a package. Two seconds later it drops a second package. How far apart will the two pack2k xtjx,2s 16ba7(o dqg3ye nkages land on the ground?

  A package of supplies is dropped from a plane, and one second later a seconda9z s h g3aetynr;h:7l0k1up 4; v-afo package is dropped. Neglecting aihef t na; 07ak;3l1:yg4sau o-vphz r9r resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flyiajie *jk -/h)a7ke, :5g7p)xinvvoph dj xf+3ng horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location ofoh x e /)7ppad haji kn) 7:i*gx3v+ev5,jf-kj the plane will

  The acceleration of gravity on the Moon is only one-s/liz + *f5 qu/hm49dff cjy;jtixth of that on Earth. If you h j;ufmjhy/5lc4z+*ifq t9/fdit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level roag *5 nclpll(d9d and pass a car traveling at 45 mi/h. The relative velocity 5l*g9lnlp(c dof your car to the other car is

  You are trying to croslmvr0sctkwk4o)w 6 ;t* a(tb )s a river that flows due south with a strong current. You start out in kb)4r6 *sca t ;(lt)k0mwvwto your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in stilk+i awe0f lt*y)i6 /axl water. How much time will it take you to move 12 km downstream, in *it fiax/a+kl)w0ye6 a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 wb.(y 4ei ;k5o.xmfcsdegrees below the +x axis. The y compon4 wb.x5mf(iceyks o;. ent of A is

  If a ball is thrown with a velocity of 25 myl 04 bzs:z5fv/s at an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a direction north of east9xsj,vw5/h ta and you end up 2.0 km north and several kilometers east. Ho/v9jah swt, x5w many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of6tgpopj; 1nknv0tu 18 its velocity is 8.00 m/s. The angle be8k6pn j0;t1ovg1tu np tween the direction of its motion and the x axis must be

  A 400-m tall tower casts a+k d 88riz1hro)u:dr s 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizodds1u)ri:+z o rk88 rhn?

  Two vectors A and B have components (0, 1) and (-1, 3), ree+yqrkf,vvks oz ;6rue: tf178)vwe/spectively. What are the component 7 ert8wvrsq6z ;of)1ef k/eu,kv :yv+s of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1,c f9ru 8,*cnix 3), respectively. What is magnitude of the sum of these two vectoin9* c frucx8,rs?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is tjlhm vgm2693i- 2ufq mhe magnitude of Cg2v2l69hfi3um mjmq- ?

  A car travels 20 km West, then 20 km South. What is then 74lsse wa(p8 magnitude of its displacemenwnsa8e4l7 (s pt?

  Three vectors, expressed in Cartesian coordinatesc5 ;vi:anh: hp3 fj3cb, are
S = (-3.5,+4.5)
T = (0,-6.5)
U = (+5.5,-2.5)
What is the magnitude of the resultant vector S + T + U ?

  Three vectors, expressed in Cartesian coo;d8t3i;ou 3iy8 wjsb2l cd/)o d:d jcdrdinates, are
S = (-3.5,+4.5)
T = (0,-6.5)
U = (+5.5,-2.5)
What is the angle of the resultant vector S + T + U measured from the positive x axis?

  If vector A = (-3.0, -4.0) and vector B = (+3.0, -8.0), w -wujym*n8 l*ohat is the magnitude of vector C l-*mjyno *uw8= A - B ?

  A runner runs halfway around a circulavo: mjoz1 974 (e9ddlygebp0f r path of radius 10 m. What is the displacement of the jogger?z 9 4ve1y7dg9bdo:pmo ef0lj(

  Two forces are acting on an object as shown in Fig. 3-1. What is b03zi f6 p9stcthe magnitude of s b930tz 6fcipthe resultant force?

  Two forces are acting on an z*, voqx69ywx)g5a3szjqil3object as shown in Fig. 3-1. What is the direction of the resulta*gsqzl z6 j,x wqxv3 5iy93a)ont force?

Vector A is 5.5 cm long and points along the x axiso+ 7 tbm5.frzz. Vector B is 7.5 cm long and points at +30e to tf.or 7t5b m+zzhe negative x axis.
(a) Determine the x and y components of Vector A .
(b) Determine the x and y components of Vector B.
(c) Determine the sum of these two vectors in terms of components.
(d) Determine the sum of these two vectors in terms of magnitude and direction.

Vector A is 75.0 cm long and pointb11snfr*5 h )zdjq y/as at $30^{\circ}$ above the positive x axis. Vector B is 25.0 cm long
and points along the negative x axis. Vector C is 40.0 cm long and points at $45^{\circ}$ below the negative x axis.
(a) Determine the x and y components of Vector A .
(b) Determine the x and y components of Vector B .
(c) Determine the x and y components of Vector C .
(d) Determine the sum of these three vectors in terms of components.
(e) Determine the sum of these three vectors in terms of magnitude and direction.

  A stone is thrown horizontally-((5d0 jbg cu pir fbpw6rz4 2sjg5f.e with an initial speed of 10 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the topu f.g z cfgs5(4-0wj2 rid65eppb(jrb of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a vby+g,o ,kaut;w89lrv8a--ne /c wwr relocity of 10 m/s, from a bridge. It falls 20 m ;-w ,olb,g aurvrc+tkwn/8 -9y ra8we to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above th7-e :.ld, niv9 zpr/: asxt1spasp ca-e ground, strikes the ground ,/s x.7:1 a-s-p: t sa9 rncpvzaldeipafter traveling horizontally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed qr v3p(x;e4hkqhbr; 2-vd z0eof 12 m/s at an angle od(ev x- e p;4khq;q0r2v3hz rbf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into the jump with a spq 4(,vsno,fsh 2th6 imeed of 12 m/s at an angle of6h4os,vfm2 t(, inqhs $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 62*tpmoiz) eg a,b52.yug j*lz0.0 m/s at an angle of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched witx ul khrim4:l684aod9x- .q* hfr c.eyh an initial velocity of 60.0 m/s at an angle of $30.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an9pn n) vpel31p6qo +srgle of $30^{\circ}$ below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below?

A projectile is shot horizontally at 23.42ur chow*l+l .pq7u7 m m/s from the roof of a building 55.0 m tall.u7o mp7l rw+lu .q*2hc
(a) Determine the time necessary for the projectile to reach the ground below.
(b) Determine the distance from the base of the building that the projectile lands.
(c) Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground.

A projectile is fired from ground level with an initial speed of 55.6 m/s at an nirp ,hwu-hykf o1o5+ hp7f*2anglihfop 7p15*h+,y2fwn-h ukroe of $41.2^{\circ}$ above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.
(b) Determine the maximum height reached by the projectile.
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height.
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height.

  On a calm day (no wind), you can run a 1500-m rac l7aggqo 49,jje at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, the time it would take you to finio 7, g4g9qjlajsh would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 9q)- tmljua5t m/s to the West. The plane's spe5 aultm-9) tqjed relative to the ground is

  A plane is flying due South (2oee0*7ss)z) c knbwsyc a6f8 $270^{\circ}$) at 500 km/h. A wind blows from East to West ($180^{\circ}$) at 45.0 km/h. Find the plane's velocity with respect to the ground.

  An airplane with a speed of 120 km/h is heade.)t1qvv d0lb tpif7bp+l0z9yctw/ l6 d $30.0^{\circ}$ east of north in a wind blowing due west at 30.0 km/h. What is the speed of the plane relative to the ground?

  A fighter plane moving 200 m/s horizontall.mgbla5h+ v/9 bibh1ay fires a projectile with speed 50.0 m/s in a forward directiohlga5a 1hbvm9/.bb+ in $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in still water is 8.0 m/s, is directed acdh1.2so1 n gj0 sz+igxross a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the riverods+ ni2xj.01 shz gg1?

  The driver of a motorboat that can i:zw :4uai zsh6cv 50wmove at 10 m/s in still water wishes to travel directly across a river 1.6 km wide in which the current flows at 5.0 m/s. How long will it take to cross thecsz5ih: a6:0ziv uw4 w river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to traveqiud ny1tk1+6l directly across a narrow strait in which theyk 11u n+6dqit current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a ri4.wp13d j knsle u8cq*ver 200 m wide reaches the opposite bank in 6 minskj41 uw.cl nd8* qpe3 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reac/ 0uia )nm+5dar; zowvt0/irlhes the opposite bank in 6 min 40 s. Shen5 ruzo0)l ;/a/i rid mt0+avw is swept downstream 480 m. What is the speed of the current?

A boat, whose speed in still water is 1.75 m u37qrcm3 ejb k7v:,.pshzl6o /s, must aim upstream at an angle of 6cu m:zql7vrb 7ep.s ho3jk, 3$26.3^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) Determine the speed of the current.
(b) Determine the resultant speed of the boat with respect to the shore.