Which one of the following is an example of a vector qua-rh 61l+ x atcco-wqa+ntity?

  Which of the following operat;w )uk2 obp6)zqqv5l kions will not change a vector?

  Which of the followingyce km4-1 ynz, is an accurate statement?

  The resultant of two vectors is the smallest when the angle between them iontmbj d 0dfr*2ja ,6hyea+ q/,4wmf5 s

  Two displacement vectors have magniap43xa2cq8*lak s 9n m9 ode-mtudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitudeo4laaq*k-28pacs m 9 d3xem n9 of the sum

  Two vectors, of magni4ioe )6)ut kqytudes 20 and 50, are added. Which one of the following is a possible4uqo) )et y6ik answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object wko.yup5nxl2kqo.0f 4j) 5zein directions that a5o2pnuf4. ykklw05 .joqxze )re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknz5, 7dw sney7 1wpkvn8 g9nf(town vector is

  Ignoring air resistance, the horizontal compone6gnpe,8)nl :f k;jzkuvj4*s e nt of a projectile's velocity

  A ball is thrown with a velozeozl+/x c 2y-city of 20 m/s at an angle of 60e above the horizontal. What is the horizontal component of its instantal-y +xo2zez/c neous velocity at the exact top of its trajectory?

  Ignoring air resistance, the3nea ve +*7rqospx)e-/8g. smbs8 jjr horizontal component of a projectile's acceleration3 -j+87o erg es*/). qma bv8pnesxrsj

  A soccer ball is kicked with dgy3ne6 *;xdt a velocity of 25 m/s at an angle 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 ly + 5p/8em8 *wjxtj 5(yyv:fpq7vxnxis directed anti-parallel to the velocity vec 8+* :vpn/t(eylm v5xjwy7 8yfx5qpjx tor,

  If the acceleration of an o/jp,mvw4g 6b ibject is always directed perpendicular to its velocity6 mgv,/j4bpiw,

  At what angle should a water-gun be aimed in order for the waxu2 *r7/mkgk 6ak7o*jyytf/f ter to land with the greatest horizonta2xmuk ytra*f 6ygk// k*7jf o7l range?

  An Olympic athlete throws a je+ lx* l/.bkfixs:o9;be- f zaavelin at four different angles above the horizontal, each with :be/*xa f.k;lxosi lfb+-z9e the same 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 the ball leaves your6lb7nwx vwr6y 7iqi3vf) /eb. hand with twice the velocity nq v7i3)f7webb xr6.w6yv/ l iit had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed ofd+ogl8l. o)z-)abm c h 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 goajmy2rwj ;ty2jkz ,(x ygpg:++l attempt reaches its maximum height, how does its speed compare to i+ tjyxy p;2+ gzmwjkjy,r 2(g:ts initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a bal:,tc9eoes6lumg0 ius80 a m- nl is dropped vertically. Which object is traveling faster when mimu:ug9te -ae,0n0cos l6 s8 it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet isj/dk*gtu5tde0 jr5 : v5; litg dropped from the same height. Ignore air resistance. Compare the times of fall of thtl /:uijet*g5dvd;r5 k 0t j5ge two bullets.

  A plane flying horizontacb(: eqvb7i5 omo 8pp o11esd;lly at a 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 wii d5m be1:oeps1 qv87 bpooc(;ll the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a2 d-btb (bm-cf second package is dropped. Neglecting air resistance, the distance between the falli -fcbm2(bt-d bng packages will

  A pilot drops a bomb from a plane flying horizontally at a c4fl2n a s s/;lza*tx6monstant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of t s4;z* 6aalmxfn2lt/she plane will

  The acceleration of gravity on the Moon is only :t r1-zi: nitae-5utj y+ue m8one-sixth of that on Earth. If you hit a baseball a 1et 5+m-yijutn iz :8-:etruon 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 straxx2v*ts)mg/zdkq 8 c/f;vrf7 ) r qx/uight, level road and pass rmv/)7 tf /*rx2qk8sf qz guv/xd)c;xa car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a 3g 4wa+x gu,avstrong current. You start out in your motorboat on the 3g gx+w,au4 aveast bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 kmy l+neuv5r.hd/.ijs+ /h in still water. How much time will it take you to move 12 km downstream, in a river flowing a+yn+s.jd.r5lih/vu e t 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 3cv40q -orkij n,;plh30 degrees below the +x axis. The y4i;0clvropk3 h, j- qn component of A is

  If a ball is thrown with a velocity of 25 m/s at an angle ofuj3yukv4d)jum;opd7 kej9 4- $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line 3(z4*2g 0o9shs hijg,qmzjbn in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east2,zi*g s oz3j 0m(94jbqnsghh have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity gm siqpu74h,/ dc(ic, is 8.00 m/s. The angle between the direction of its motio,m /7i4pqg,c( cuhsidn and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a le83-g 4d3o;vqzeclojl (jp- z+ vm+g oovel ground. At what angle is the Sun o3qv+ goeol;p8v -lco(d3+j4 mzjzg- elevated above the horizon?

  Two vectors A and B have components (0, 1) ata:81 b dft6royr) cp)nd (-1, 3), respectively. What are the components of tp6:a)fd8 rc rb1o y)tthe sum of these two vectors?

  Two vectors A and B have compone// ndfn4qck 9j) ,litrm)8d dhnts (0, 1) and (-1, 3), respectively. What is magnitude of the sum ojdnq)/hdr894t ,fdknm/ i)c l f these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is s . jyg3fj5r; auio;y9the magnitude of C ?3.s5ygay;;i of9r j ju

  A car travels 20 km West, then 20 km South. What is the mav8voha40:a5 b t:fwz5s rcpb,gnitude of its displacement?c55 :pt8rvbvo ah0 zsbf,:4 wa

  Three vectors, expressed in Cartesiof0m9lzhi u69)pr s.n npo-uq6ok+-f an coordinates, 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, expressede1ep n56l)lyh g q2j2q in Cartesian coordinates, 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 vecto aego-l2w3:a f u6q -i+ne +qehv+u:icr B = (+3.0, -8.0), what is the magnitude of vg evw6 :3ifea+u+qn2- uqhoi+e: -alc ector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What0oj7. tt xpyd8r-l e+m is the displacement of the joggerl8je .rdty-x7po+m t0 ?

  Two forces are actin)snyv 5zg2qjbc :*r(b g on an object as shown in Fig. 3-1. What is the magnitude of the resultant fo 2( *bnr) v:cyqgb5zsjrce?

  Two forces are acting on an object as shown in Fig. 3-1. What is the directionbezl/o*duva: 0 o.x2 g of the rad 0zvoo:be /2glu.x *esultant force?

Vector A is 5.5 cm long and points along the x axis. Vecg4v;hahe-j y dm,1gn. tor B is 7.5 cm long and points at +30e to the negativj g4eya mg 1hhdvn,-;.e 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 a4bkmg,*dnp/w /mj uv* nd points 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 with an initial speed of d4den w(ehq)2.e/woa10 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the heigh de ew2 aw/eh4qno(d.)t of the cliff?

  A girl throws a rock horizontally, withp e(-.muqk s*t a velocity of 10 m/s, from a bridge. It fall(*-. usq kempts 20 m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m aue7gz,ahwab3w 3em0v 0 8e(iubove the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it throwua33v70z0bmw(uee8w age h , in?

  A jumper in the long-jump goes into the jump with a speed of 12 m6eyx(1gp d-da/s at an angle of dgx- 6d(paey1 $20^{\circ}$ 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 speed,m 1f 9xx,z:;ewu ph oyrowk84 of 12 m/s at an angle rk y,fu9:zxwoe18m; wx4o hp ,of $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity odviodh xl 1 x2tf44+l+f 60.0 m/s at an angle of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veloccv;;:jqd:hqrbz,ll r4z -d 0 :ipw5pvity 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 axpk1 ae y08h u:g*pbb9jl 0)ybngle 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 23.4 m/s from the roof b72.jh* c, ykva;eyn oof a building 55.0 m talnkveyj7 b* c2a.,hy ;ol.
(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 ajb h.r-5g+ypqxzopg7.a sy ;9t an p+j gz; bsq9 7-yh oa5.yprx.gangle 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 race at a velocity of 4.0yqwgd- wg4k+ xjl ))fp2 )zq/h m/s. If you ran the same race on a day when you had a constant headwind which slows yoq/djq- yw l)+))f xhgw4p2zgk ur speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wirxi y5urpb rd0b+:pg s4 uc9m :+d2ws1nd of 50.0 m/s to the West. The plane's speed relative to the groun +dp ur2:ur sgc0+ywrx5 bibs9pmd4:1d is

  A plane is flying due Souxxg2:;zb9cj b*vsin n p)u5 )pth ($270^{\circ}$) 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 vkzc8mhtvf )2 b ,76vhv +/eelof 120 km/h is headed $30.0^{\circ}$ 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 9ukx3 70rq,ed yti fe.-a 4g6ivbj+nwm/s horizontally fires a projectile with speed 50.0 m/sra7i-xfeb4vun ,w3k d0.ye9+6jt giq in a forward direction $30.0^{\circ}$ 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 mvm5wgwwyhqy93o :( i 5/s, is directed across a river with a 9ymqwivgwy:oh5 (3 w5current of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motoej 9 ++wsakg6 ,y. drnwbo/s(2njklk:rboat that can move at 10 m/s in still water wishes to travel directly across a river 1.6 km wide in which the cu9,kb +: kk lo+/j6s nwyw.ajgs(red2nrrent flows at 5.0 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move att;,-khy70 b pqtwx:qy 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver heyttbpy ; 0k w:h,qxq7-ad the boat?

  A swimmer heading directl5y3b/f j muq3gy across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is s3fbmqjug 53y /wept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across;cbgoz 6av9h0 a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the s gzo6va;bhc9 0peed of the current?

A boat, whose speed in still watntd:65tt bvu /er is 1.75 m/s, must aim upstream at an angle ofu 56dt/bt: vnt $26.3^{\circ}$ (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.