Which one of the following is an example of a vector quantity?9q6ey50swi+n(za o la

  Which of the following operations will mrt)lk5e3t8z v0tbyobv 8x jd)d;;6 gnot change a vector?

  Which of the following is an accurap0fe7vl0me e y3j hl,:te statement?

  The resultant of two8cp2mcfzw(z/ (i 2kca vectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7rnvcvrw fec* q) (. (rjm xm3mmlm.(32.0 m, respectively. When these two vectors are added, the magnitude .v q*c fm.3 xr2)l v(mmm(mr3wjr c(enof the sum

  Two vectors, of magnitudes 20: 4 q3cicafd i+y(sfs- and 50, are added. Which one of the following is fsy:f( d-34+cicaq isa possible answer for the magnitude of the resultant?

  Three forces, each having a maguv;v:vb3:zeg s5 dka3 nitude of 30 N, pull on an object in directions that v ;a:5egkvzu 3s3b :dvare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown v+f6/jexx l f2mector is

  Ignoring air resistance, the horizontal compoye*l uz -ym:l u*cu87x ex;: .xdz1bzlnent of a projectile's velocity

  A ball is thrown withgt .j nd9x9b 3d /bysr+phd8iz-2ca 9c a velocity 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 resista,z.rzu6fe , ,ztaxn(tnce, the horizontal component of a projectile's acceleration ( z,.zuxeatt,rz,6fn

  A soccer ball is kicked with a velocity of 25 m/s at an angle o etj/,mr o3jb+c8 0zykf $45^{\circ}$ 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-parallel to the ve(b1r7 l8wg) h8ulpzuflocit7zgwlfuluh(8 1 )prb 8y vector,

  If the acceleration of an object is always directed perpendicular to its +nd; s/opiw 7ij(mf,h velocity;id in (/s m+,pw7hjof,

  At what angle should a wateh 2 vt0oqr2blp d5hdcvw19f. 1r-gun be aimed in order for the water to land with the greatest horizontal range.0v2oc9phlv 1r5ft d2w1 h bdq?

  An Olympic athlete throws a javelin at four different angles abopby8silaz)o- 8mwaeh/ ; f 0)zve the horizontal, eayhs0/)fab e ;am p -o8i)wzlz8ch with 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 thpxhrdn vj 9*r3uey j:b ;:pd,)e ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) wou9 pdd:,rep :bh3 yxun);j*vj rld be

  A ball is thrown at an original speed of 8.0 m/s at an angle ok7 d (;b wjrclhfl6qw kz0p hg5y+0j97f $35^{\circ}$ 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, how.sa + hebn+/mt does its speed.e bsnma+h/t+ compare to its initial speed?

  A stone is thrown horizontally from 0yl( lf72o5x(p4vee(bx; sxsb-ny f sthe top of a tower at the same instant a ball is dropped vertically. (o5n xsfxvf(l e-blesp(by0sx; 724 yWhich object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is dropp3f ( zpgw*kfj0ed from the same height. Ignore air resistance.fwkp*f (j30 zg Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 113.0 m/s and at an elevation of 1w h*l 18si i2zoj/:mzc rep0gjy5 4v,y35 m drops a package. 6.5 seconds later it drops a second package. How far m j:vew5 iyl z041r8zs*cip2 h,ojg/y apart will the two packages land on the ground?

  A package of supplies is dropg /j pi)nmu8kc1ef ox-;gbv 3*ped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling;b/- n3i*oku gemg cv) 18jfpx packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Neg0jzkf ( hqjeg*.j2 4qwn9 f1ajb9mz *mlecting air resistance, when the bomb hits the ground the horizontal location of the plane wjjm ma(q4nz1e k w09q.fb*z92h jfjg*ill

  The acceleration of gravity on the Moonh+s3--z: e2pt;ka jl 9ppzcah is only one-sixth of that on Earth. If you hit a baseball on the Moon with thel;ez - pp -th2paj:+zk9c ha3s 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, le5l (cq/jho7uv-x xlf 2vel road and pass a car traveling at 45 mi/h. The relafxhux275ll-( /jqc o vtive velocity of your car to the other car is

  You are trying to cross a river that flows due south withk5nk0i)g fpk 5 :lnm1eps16lt a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from yo1:pkpitl )m55g6k kn 01fl nesur starting point. You should head your motorboat

  Your motorboat can move at 30 km/hgo* 6fnj(zb) p in still water. How much time will it take you to movenp*o(gb ) z6fj 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle oft dnvigy(l7 j)2w .qgflf*g f9n 1zs6, 30 degrees below the +x axis. The y componesn7(q.2v*t) ygw6fgfflijzd1 ,gl9 nnt of A is

  If a ball is thrown with a verhmr( n.: e:og hfi94ilocity 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 north of east and you end witih h(su;h 4/s7jjace(p11 up 2.0 km north and several kilometh1ew/ si4ihjj h 7(pt(us 1;acers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its vel1k loco gjmbn(r* 08w4ocity is 8.00 m/s. The angle berl8(jcm ob k1wn*o 0g4tween the direction of its motion and the x axis must be

  A 400-m tall tower cast0p 5d:x1xpbso am11h us a 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizom05xus a ppdbh:1xo11 n?

  Two vectors A and B have components (0, 1) and (-1, 3), x5g ud (- pf3esnvpz58respectively. What are the components of the su-updpe5 s(5gzfnx 8 3vm of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), i/t npo*:pa t b7 alqno7(yy0;respectively. What is magnitude of the sum of these two vectn bypat*ao( qy n/;770pol:it ors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magniti9ixf b/ 4s:iq ++0ntt5ew3fq6z 1suujtf2ioude /z93i b6 ufsqit405itnt s ifoj +:e2+fu1xwqof C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of.bw;r37 b8;o3jgwe mf p1sgqm its displaceme8b3gj.1bo;fmwrqm gw; pes 73nt?

  Three vectors, expressed in C(i(rchq4 kl o/o+co*xw0 ua 7cartesian 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 Ca nl*srq 2pf,.jrtesian 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 = (+3.0l trjal,9e(g8 i x.,od, -8.0), what is the magnitude of vector C =.,l i9to,8 xgrdjlea( A - B ?

  A runner runs halfway around a circular path of radius 10 m. Wghch )a3h:oyh qqt51 -hat is the displacement oh5:h cqhay )q-got31hf the jogger?

  Two forces are acting on an obje90bzzm kc,jn9 tx,en )ct as shown in Fig. below. What is the magnitude of tez,j 9nknct ,z9m x0)bhe resultant force?

  Two forces are acting on an oerezje vyc7csf8w. 8h04:29p tegls-bject as shown in Fig. below. What is the direction of vrc82yf: -ec g. tp4hweslze09ej8 s7 the resultant force?

  Vector A is 3.6 cm long and points along the positij p/m;/mxard) u1ec ihw :rx*7ve x axis. Vector B is 7.7 cm long and points at;ijaxedr c mpmu:7 r/)*w 1xh/ $+50^{\circ}$ 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 78 cm long and po4ktq,t(-joa n ints at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 36 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 horizontally with an initial speed of 23 m/s from8esq.p/9rmznw9 wkni) nb0.d 4v b,gr the edge of a cliff. A stop watch measures the stone's trajectory time from tn0k./p9snw9bqz,mb w rgndr)4ve i8. he top of the cliff to the bottom to be 4.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 9 m/s, from q*h akqipchz 9 w-6--ka bridge. It falls 21 m to the water below. How far does the rock travel horizoc i6wq-q-kha k*h-pz 9ntally before striking the water?

  A ball thrown horizontally from a point 26 m above the ground, strikes tjh c:,wdjw1jet6:ge6he ground after traveling horizontally a distance of 23 m. Witt:ew6c61 j,h djjw :egh what speed was it thrown?

  A jumper in the long-jump goes int7 1.y k rid un 8.g2mchx37f4yjbkhz4go the jump with a speed of 12 m/s at an angle kfh. gm ji 48yrb2cu7 gzhy. 4n31k7dxof $20^{\circ}$ 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 of 12 m/s at an ang69ekw.u zhk6ao5f0jl0pwf 4fk c 3t 2qle olk0f c6w9k4ua 0e. z5op2 f3kwhftj6qf $35^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial veloz8y ytz.t4n (o3:xwj +bpi1doi 1 zxv4*vsg* ocity of 42.4 m/s at an angle of $40.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity 2b/g1 l/s. j29 wjveeozdje,/ht4gb97htf utof 27.9 m/s at an angle of $35.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglexf*l w6z d8-ri* wnm2q 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 wxxn ir)6+xd 2horizontally at 20.0 $m/s$ from the roof of a building 33.1 $m$ 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 groundu/i 8mmir2svcv84 u*d level with an initial speed of 56.9 m/s at an angl8iuu mi8vs4 crm/*vd2e of $37.5^{\circ}$ 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 run a 1500x ljk3-2 7strg-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 slo g j7xstkr32l-ws your 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 wir.omu 4gqye14nd of 50.0 m/s to the West.1.u4ye go4mqr The plane's speed relative to the ground is

  A plane is flying due South (o5,1zitm62/1 bx ysgwvs2iwf$270^{\circ}$) 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 headipw )tanja5 ;-ed $30.0^{\circ}$ 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/srt9p7bvdqck 0w ti6 /* horizontally fires a projectile with speed 50.0 m/s in/9d* c6qt pi0bwtk vr7 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 directed acroi13pavx f )ot;u1ne 5css a river with a current of 6.0 m/s. What is th p)o1a5c ifu1e;vt3xne speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 16 m/s in sier45.2tv;(aht f qa; q ofc(jtill water wishes to travel directly across a river 1.7 km wide in which the cu fv(to(h;qft4q 5c2;irje a.arrent flows at 6.0 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 2se5jdw dfkm9 a,5xegk.v1q1wishes to travelqwe .sx2 k51dge,9jkvfam 5d1 directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposdmen dx6d::(p6mca(7 ljeja.ite bank in 6 min 40 s. She is swept downst766jam(e :(d .emcpx: ddn ljaream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the oppos 4hdn0upx-+er5z o04jf tnb6h ite bank in 6 mrfb40n 6hu 5+ p4oedhx0-zjtnin 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.44 m/s, me6)k sfa 8kfm4palu3-ust aim upstream at an angle ofusef8kfkaa3pm6 l)4- $17.2^{\circ}$ (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)  $m/s$