Which one of the followisj,z0l qqi86 fmgmg2(ng is an example of a vector quantity?

  Which of the following operations will njzwoxi, i a6x39;nurn:5q o:ch a.z253ajtxf ot change a vector?

  Which of the following is an accurate sta qk3z en/*iy *szg+bz6tement?

  The resultant of two vectors is the smallest when the anglaa ;nwq eug*y7fn;/n 0e between them is

  Two displacement vectors have magnitkap 6 +8 oap0gj1t9fnfudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of thfp atjan9gk op+8610fe sum

  Two vectors, of magnitudes 20 and 50, are added. Which /i8rlq(10 litpdc 1wwone of the following is a po cliw wrd(qptl08i11/ssible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in d*)qskp : ss,fcudya5 vcp171 airections that areas: 1ps ,caqdk*5 sfc )1y7pvu $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowntmiz-x, +, 1/yjutorv vector is

  Ignoring air resistance, the horizontal component of a projecti1 n mx,1 ,k2sd.c/pbgminr4xxle's velocity

  A ball is thrown with a velncv7rxt6uv *- ocity of 20 m/s at an angle of $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal component of a projec7ll gofbg*2mzh 7(5lutile's acceleration7*mzlg5g h 2b7fulo(l

  A soccer ball is kicked with a *gmlf6t tik1: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 is direrq.sfy) vlbx9 * ogb*s7kh6x wk*t /)gy61cmjcted anti-parallel to the velocity okr71l)yjgf . /*bk* x*syq6b )gx9v wchs6mt vector,

  If the acceleration of an object is alwags4d5al:mck 4; pa cc,qg*0r vys directed perpendicular to its velocit4, :pcqc5* ;4rakdva clg0mgs y,

  At what angle should a water-gun be kgj/0(: up bbdt 3bpd7aimed in order for the water to land with the greatest horizonta(gbd/u0j p 7bkd3:ptbl range?

  An Olympic athlete throws a javelin at four different angles above the horizon kots:n4x arbt1* xv5.tal, each with r bkvt 5.naxs1:t*x4othe 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 balf /mhq-to0ayx q;q 0n1l for the second time. If the ball leaves your hand with twice the velot/q1 ym-xqhq0o0a fn;city it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original sytr .m6gb wplb6 +mb9-peed 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 heighwg2k+omn su::cty d:6t, how does its speed compare to its ini::ydo2: g wnmkcus+t6 tial speed?

  A stone is thrown horizontally from the top of a 9ppch , n5.vkftower at the same instant a ball is dropped vertically,5hvfckp 9 .pn. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a secondygc*g vup z./- bullet is dropped from the same height. Ignore air resistance. Compare the tic -ygp *uvz.g/mes of fall of the two bullets.

  A plane flying horizontally at a speed of 55.0 m/s and at an el:gk6mvv7* n l8iarot, peh.,mdq(2 yaevation of 130 m dpq, 8,mgm6*v:d nhaoat.er 2yli kv7 (rops a package. 6.5 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from 9 ee8dp+5js.1cgahzg a plane, and one second later a second paccdp. e8g+ez sga j9h15kage is dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed, (x (ne -efbxt0sxtb1. Neglecting air resistance, when the bomb hits0xbe,fn(tb x( 1esx t- the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of+*76y fll; x6pwr zu, bf/rbfm that on Earth. If you hit a baseball o ;y * 7b bmlr6z/xfu6lwpff,+rn 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 roaqtp e 3xvn/5/nlbs 8n-d and pass a car traveling at 45 mi/h. The rellp/b5xv n t/-8 nnqse3ative velocity of your car to the other car is

  You are trying to cross a river that flows due south witzp -tr uvm*(rx2x8py+h a strong current. You start out in your motorboat on the east bank desiring to reach the wexr ppmr-uz+8 2y*(vx tst bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How mu/ -qsf3*feu wxch time will it take you to move 1* -x3sf u/qfew2 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m33 5iz y3tl7yqsg7g5uu 1qgd- azlda8 at an angle of 30 degrees below the +x axis. The y componi ya gltl3-gzu1 7u5da dqzgs85y 7q33ent of A is

  If a ball is thrown with a velocit2 m k1ly632ppixz:d9o5li ql hy 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 direction norey.zqhxve)z39 7c gci-l p6h-th of east and you end up 2.0 km north and several kilometers east. Hy6-9ccqheze 7pzx ih)v3-.glow many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x *dudx3f4u( a inm,1nb component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must 3(d un4*u,xa1d ibmfnbe

  A 400-m tall tower casts a 600-m long shadow over a level 5juwz ( 016fokhfyfo7ground. At what angle is the Sun elevated above the 16w jfofyz0 k57(ouhfhorizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivelyvl8sdne yc9xsd 1*r; /y xwq*). What are the components of the su9)nc *eyxlrdv;dysqx/w * s18m of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), resp-(* v+sl t j-xstz(yajectively. What is magnitude of the sum of the-ss- t(l*t(jxa vyj+z se two vectors?

  Vector A = (1, 3). Vector B = (3, l d dr1*/c,rej0). Vector C = A + B . What is the magnitude ofd*d/, crl jer1 C ?

  A car travels 20 km k8 hpt84*fni oWest, then 20 km South. What is the magnitude of its displace n8o4fp 8*tkhiment?

  Three vectors, expressed in Cartesia 7 j3p;qzdp6dpn 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, expressed in Cartesian f1 .p(0y3mschznv w7 b0a; keacoordinates, 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, 9v* 4brf- fgvv-4.0) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A - B ?fvfr-9v4b *vg

  A runner runs halfway around a circular path of radius 10 m. Whaaqtl ,y1vp05p a,u-s xc/mnj*t is the displacement of the jog/sp,yxm a vtucj5pl-q n0a*1, ger?

  Two forces are acting on an object as shown bv8i j(-yp uld;0o1 (li ;qp /vgeu*riin Fig. below. What is the magnitude of the resultan/gdebyj ip1(vi*o- v0 q8;r ilp;( luut force?

  Two forces are acting on an object as shonm ;+mv dt8sy7wn in Fig. below. What is the direction of the res yvd;8n+s 7mtmultant force?

  Vector A is 3.2 cm long and points along thelst8k6 nd-slh,aahdq)-t8- z positive x axis. Vector B is 8.3 cm long and p6 t l8- alds k-8ht,hnsq)d-azoints at $+52^{\circ}$ to the negative x axis.
(a) Determine the x component of Vector A $A_x =$ (数值)  $cm$ and y component of Vector A $A_y =$ (数值)  $cm$
(b) Determine the x component of Vector B $B_x =$ (数值)  $cm$ and y component of Vector B $B_y =$ (数值)  $cm$
(c) Determine the sum of these two vectors in terms of components. $R_x=$  (数值)  $cm$ and $R_y=$  (数值)  $cm$
(d) Determine the sum of these two vectors in terms of magnitude  (数值)  $cm$ and the tangent value of the direction angle (measured from the posive x axis rotated in the counterclock wise direction) $\tan \theta = $  (数值) 
Please only fill in numerical values in the above blanks!

  Vector A is 69 cm long6wrv k/jl yc/+ and points at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 34 cm long and points at $45^{\circ}$ below the negative x axis.
(a) Determine the x and y components of Vector A: $A_x=$  (数值)  $cm$ and $A_y=$  (数值)  $cm$
(b) Determine the x and y components of Vector B: $B_x=$  (数值)  $cm$ and $B_y=$  (数值)  $cm$
(c) Determine the x and y components of Vector C: $C_x=$  (数值)  $cm$ and $C_y=$  (数值)  $cm$
(d) Determine the sum of these three vectors in terms of components. $R_x=$  (数值)  $cm$ and $R_y=$  (数值)  $cm$
(e) Determine the sum of these three vectors in terms of magnitude  (数值)  $cm$ and the tangent value of the direction angle (measured from the positive x-axis rotated in the counterclock wise direction) $\tan \theta=$  (数值) 
(Please only fill in numerical value in the above blanks!)

  A stone is thrown horizontallyw q5z.)/dn.. tag av2qhxjwo * with an initial speed of 21 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 height o2x )w av ./noad5. hzqqwg.*tjf the cliff?

  A girl throws a rock horizonta7p 66u)nb ;bypll9hc:u e9due lly, with a velocity of 15 m/s, from a bridge. It falls 12 m to the water below. How far doeyep7:l6pb6bd)u; 9 u9hl uecns the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 19 m above the ground, strikes ;5 */x fmnn;ntm g0bkcgfms95 the ground after traveling horizontally a distance of 15s ;tb*n g;ncgm59xf5m/ nk0mf m. With what speed was it thrown?

  A jumper in the long-jump ggs (w35; ,yc is5cropaoes into the jump with a speed of 12 m/s at an angle oar5i;s 3s c5p,g (cowyf $20^{\circ}$ 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 wit3hg *(tt zf50ckfqw9ih a speed of 13 m/s at an angle g (fi3 hw*ft0kz9tc 5qof $24^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched wi8v (hw ac7pw+nth an initial velocity of 52.2 m/s at an angle of $11.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 43.3 m/s at z8vt pe5t/c o:an angle of $41.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angy 7ye- qo9lq7/o;d6v v5ehmafle 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 horizontallyi*.iue t8w *qn at 23.6 $m/s$ from the roof of a building 49.7 $m$ tall.
(a) Determine the time necessary for the projectile to reach the ground below.  (数值)  $s$
(b) Determine the distance from the base of the building that the projectile lands.  (数值)  $m$
(c) Determine the horizontal component of the velocity just before the projectile reaches the ground.  (数值)  $m/s$
(d) Determine the vertical component of the velocity just before the projectile reaches the ground.  (数值)  $m/s$

  A projectile is fired from groundn +vz s.(ol k6e i9wis5-n6ajc level with an initial speed of 57.0 m/s at an angle of9zki+wln6j( .i- os6es 5anvc $46.2^{\circ}$ above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.  (数值)  $s$
(b) Determine the maximum height reached by the projectile.  (数值)  $m$
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height. horizontal:  (数值)  $m/s$ vertical:  (数值)  $m/s$
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height. horizontal:  (数值)  $m/s^2$ vertical:  (数值)  $m/s^2$

  On a calm day (no wind), you can u i 7oby*ak7z)kv i8h-run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slowskz )a y8uib7k 7-*ihov your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air s exx/lw- 6wq4iy(xd( x;qe; expeed of 200 m/s due North, and is in a wind of 50.0 m/s to the We/e(w4de;-qxxx ley6q ;xwx( ist. The plane's speed relative to the ground is

  A plane is flying due S c y/:1gbiq,jdouth ($270^{\circ}$) 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 headed/awf nx u(gd q6mxo2eas*0+k6 $30.0^{\circ}$ 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 horizo2yi4k o 1y-ygjoe(wy3 9uii +pntally fires a projectile with speed 50.0 m/s iny(gy2-9io1 ie3 o+kyjp4yui w 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(48 h:qw viufo 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is thef vq( o4huw:8i speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in still warec * u4h/ oauo/fr0f0ter wishes to travel directly across a river 1.3 km wide in which the current flows at 5.1 m/s. How long wiar0c /4ff oe ru0u/*holl it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wisheit18) ppg *ztus to travel directly across a narrow strait in which the current flows at 5.0 p8tu)tz* i1gp m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reachesgc 8 ks8tq tdaai,(.1x the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim8tksaq(.x,t8ci1d a g in still water?

  A swimmer heading directly ac x5fmo w6m;aq :b39r js;)snpfross a river 200 m wide reaches the opposite bank in 6 f3xmar;9j sb5;p)osn q:w f 6mmin 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.15 m/s, must aim upstream at an anroe afyq;)7,ugle of oy7q ;u,raf)e $30.7^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) Determine the speed of the current.  (数值)  $m/s$
(b) Determine the resultant speed of the boat with respect to the shore  (数值)  $m/s$