Which one of the following is an example of a vectoc jjkv8f 26ts;r quantity?

  Which of the following opera,xy axxj )0hl1tions will not change a vector?

  Which of the following is an accurib 8..e0 dujdtate statement?

  The resultant of two vectors is the smallest wh/fu)k4ko it edf1 t1o9en the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. Whepx h00f o(i,oen these two veci,0xp o(h0ofetors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the6 6jzvj ;pccxp*aaup 88f*2v o following is a possible answer for the magnitude of the resultantf8jp *pca ajpuc;6x*o z6vv8 2?

  Three forces, each having a ma9whrmu9bmq0 y3 ie. +gyj o 5yc7fa3f.gnitude of 30 N, pull on an object in directions that are bha yf79qrfy3ey903w.c ogum 5 i.m +j$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknows xk/m*w*. l)diin gk b8vwyeytc/d+.f6 cv6+n vector is

  Ignoring air resistance, the horizontal compoj:d8gpwk 0; g/ hgii2cdl 8oj*41y rxonent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle of 60e above tam1p n)3fy *dphe horizontal. Whany)d*p p 31famt is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal component of a projectile's accelerationahx 0)mcb4pz 8+zk/pk2 jhwe6z hpja6/bk+c24p m k0ex)zwh8

  A soccer ball is kicked with a velocity of 25j,wqv8:mb2psa f( r b6wn-j)v 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 is directe i91o1x:uvwm+x xmw ;kd anti-parallel to the velocity vectoixw :mm +xo11;v ukx9wr,

  If the acceleration of an obu)af* 7 w)se:e* jncfbject is always directed perpendicular to its velocity,es:)ne*)a* wucf jf 7b

  At what angle should a 6pwosg2t .3w wwater-gun be aimed in order for the water to land with the gr2o 6gwt3. pwsweatest horizontal range?

  An Olympic athlete throws a javel (ij)u y;mbxcz pci5)0in at four different angles above the horizontal, each with the uc(z ip j)my0;)b5xci 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 tqwlo/o* ,onx; he second time. If the ball leaves your hand with twice the velocity it had on your first lnoxoq ,w/ ;*othrow, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle of 3p mqcxaus3v+i:+o /y $35^{\circ}$ 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, howuar7/3 -s1svfm z+eoi does its speed co a3 1erz7uvmo/-ifss+ mpare to its initial speed?

  A stone is thrown horizontally from+ok -1s+nkm(zh:2dhlyib( em the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level groun(emizydmh :s 2 h-(ob+1 nk+lkd below?

  A bullet is fired horizontally, and at the same instant a second bullet (hw9by j-/ddcis dropped from the same height. Ignore air resistance. Ch c(wjbd9y -/dompare the times of fall of the two bullets.

  A plane flying horizon7 m8/l :1ktzd nab*k lagv ,mtb57gfrmd9ff; :tally at a speed of 50.0 m/s and at an elevation of 160 m drops a package. Two seconds later it dr;,al fm1k9d5tlmgkfnzbd7 78bg:* : /ra tmvfops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second6+sj mcsu9.-nzy kpu 1 package is dropped. Neglecting air resistance, the distance between the falling pack6sm .s- n+puck zuyj91ages will

  A pilot drops a bomb from a plane flying horizontally at a constanw9. usd9-g:ofr1stop a,0l 1y7s vq edt speed. Neglecting air resistance, when the bomb hits the ground the horizontal loca to9 1,l09 w-s:ag1efsuo.prsd7dqvy tion of the plane will

  The acceleration of gravity on the Moon is only h bzyh-b 8 7cddzwf64.one-sixth of that on Earth. If you hit dbh6f74y d cwz .bh8-za 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 epl7x7r*zc,i straight, level road and pass a car traveling at 45 mi/irxe ,7clz7p*h. The relative velocity of your car to the other car is

  You are trying to cross w;i7n;ebs (ija river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west fro7;;n e(iisjbwm your starting point. You should head your motorboat

  Your motorboat can movj+.9dedk yku4 ug1p / 3s8qwxse at 30 km/h in still water. How much time will it take you to m+ukd/q9e4.sgukx81yds3 w p jove 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x b ;i qof(:t0yyaxis. The y componq:;yoft(iby0 ent of A is

  If a ball is thrown with a vpko:9m1 nb3c gt3vx: 9e2rjdvelocity of 25 m/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 directiuggwq1x,mpr1s3 n, f5 on north of east and you end up 2.0 km north and several kilometers east. How many degrees ng1p,3mx sg51 r, quwfnorth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity is 82i.mj7-spcm o.00 m/s. The angle between the direction of its mom cos.7 2mi-pjtion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level grouno8q b9c1jga j2h 57egtd. At what angle is the Sun elevated above8oga7eg jh jctq152b9 the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. (1; kbn-yg7ld7wgm ay mcm2p8What are the components of the sum of these(1w m 8am2kcpyb lydn-gm7;g7 two vectors?

  Two vectors A and B have components (0, 1) ang z h i;ipl;ogyies,+n5 o9p+u-:l8kpd (-1, 3), respectively. What is magnitude of the sum of these two veco:pi;+ ygiil5,lkg z;-+shpupeo 9n8tors?

  Vector A = (1, 3). Ve ;3lp g2gzvfgp6p:*+ure b9t:cw xsu1ctor B = (3, 0). Vector C = A + B . What is the magnitude of C2u :v9p+ 3lu pc*:sgepgf r;twzbxg 61 ?

  A car travels 20 km West, then 20 km South. What is the magnitudeduh +zyez5e 7bnf082 h of its displacemenehz+bhune7f5 z20 dy8t?

  Three vectors, expressed in Cartesian coor0gwj k :q tp-1h,vatw0dinates, 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, expres gsqk:,mm l6++si1teqsed 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 vector B = (+3.0, -8.0), what is the magnitude o pgx m8xl:o(hx l-yoc(s1e35hf vectoryx(cpxg ( m3he5l8h1:s-xo lo C = A - B ?

  A runner runs halfway around a circular path of radi(+ hond p5 86tdi-3wq0onazocus 10 m. What is the displacement+ w ic6-n3 (antozq580dhpood of the jogger?

  Two forces are acting on an object as shown in Fig. 3-1. What is the magnitude +jx b6zfc-l; omqe8e 7hxet2:of thet8 xq+e: ;xj- obz2em6lhe 7cf resultant force?

  Two forces are acting on an object as shown inv 6;j:/ew(7m-m gxzd3 omemh*p jof9c Fig. 3-1. What is the direction of theo-;wze /7mh go(9fdm3* :jc 6pvjxmme resultant force?

Vector A is 5.5 cm long and poikq7p3 kfr i-d)5i vq).kiue-znts along the x axis. Vector B is 7.5 cm long and points atpqk-r-kv 7k i) 3feu.5zid)iq +30e to 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 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 de/-6 ;t j6 ebj2ls/k/mahh zslong and 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 horizont8ruq ya7 s7r,84xwyvcally with an initial speed of 10 m/s from the edge of a cliff.c7rx8a7ysvy 4ru,wq8 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 height of the cliff?

  A girl throws a rock horizontally, with a q 3v 5xdyq veb..u(4dzvelocity of 10 m/s, from a bridge. It falls 20 m to the water bx .eqv 4d zyuv3qd5b(.elow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above the ground, stri,jx:m./ d w+lqys k/jjkes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown?dsjx/kljyq,/m w:.+j

  A jumper in the long-j09 oxgm l,nwg7ump goes into the jump with a speed of 12 m/s at an angle log9w7nxm,0 gof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jumpq e02zop .*jgei.j c.x goes into the jump with a speed of 12 m/s at an angle of. .*oq gpe.ec0jjx2i z $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 60.0 m/s at an anglek)qhu nuqw6d:sx *5i57fn4e n of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 60.0 m/ zdou3 ic/mfkz,v1ifjp/ 0bh*i( e66 ls 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 anglei+4tfvod hji8 cxss564v /w+d 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 ofhr 3boy3jm:zn-ujg ; 0 a building 55.0 m tarnjg0o-by3z;u m h:j3ll.
(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 atz 1f(q .qqkjl, an a1(,.jqk fzqlqngle 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 velocitv0.gcwgqg8,v em1nh*ei at6*y 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 wou e 1tvvaiw*g h,c6qegm*.8 g0nld take you to finish would be

  A plane has an air speed of 200 m/kh r,t yu*1k s+ r2lizv;s6sa)s due North, and is in a wind of 50.0 m/s to the Wesh y vu,si)z +l2kstrka*;r61st. The plane's speed relative to the ground is

  A plane is flying due Shx xow: y wta(.cd8p 3wu3qp;7outh ($270^{\circ}$) 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 ia4z-jnb /cdv + o6nuw(s 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 movivy 0k2zg l6xk(:d)yajng 200 m/s horizontally fires a projectile with speed 50.0 m/s a0y 2y:6 vk)kj gx(lzdin 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 m/s, is diikk l 5j4rtxt+wds70n- j.aj3rected across a river with a current of nsk03tt lk-ja w 7ji5.xj4+rd 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move*h bmg4a 1nn zddu+gh .2hr(e/ at 10 m/s in still water wishes to travel directly across a rivehn/a.g4+* hdd (b1 mzengrh2u r 1.6 km wide in which the current flows at 5.0 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wi le w+bhm,y1v7shes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head w+elmy hb,7v1the boat?

  A swimmer heading directly ac /scl d1zfva, o6dq+s:vxzr+ u1i0-qcross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept doouzfs 1i/ -v:0vsx,q1d q 6lzc+r+ad cwnstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 / i3ecaqgph74m wide reaches the opposite bank in 6 min 40 s. She is swept do74/aipecq3 ghwnstream 480 m. What is the speed of the current?

A boat, whose speed in still water i2q vfk68wd+oo s 1.75 m/s, must aim upstream at an angle of vd oof +2wqk68$26.3^{\circ}$ (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.