Which one of the following is an example of a ye b1 xz0z*5oug ir4-lvector quantity?

  Which of the following operations will not c(e.2 ofo11ncrv omfws *1bo/: y twe9gb9-mdphange a vector?

  Which of the following is an accu8xoglu(;afz 6 rate statement?

  The resultant of two vectors is the smallest when the.uwk8d1t 5w+y ud h8 fyju .t/2lsao+w angle between them is

  Two displacement vectors have magnitudh0+ko,lzb(mp o1ona jbot ge-*:m4e5es of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of thoe*(hp:mon0zbgejmb,l k 4 o+ao5 -1t e sum

  Two vectors, of magnitudes 20 and 50, are added. Which t4*4zklz o4q uw n7nm6one of the following is a possible answer for the magnitudemq kl o*n 6wz44zt74un of the resultant?

  Three forces, each having a magnitude of 3v 8-c,1: pso8h1hflg/a9sm j:vrst tr0 N, pull on an object in directions tha-1v/fo hjms ,8:r1htgastrvc :l s98pt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the usybt7jfck :3(le;-vwnknown vector is

  Ignoring air resistance, the horizontal component of a projectio9ss +sqz2jn :+g stv1le's velocity

  A ball is thrown with a velocity of 20 m/s at an angle)r yx32 ow05grami xn0 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 projectile's acboer w)g/(yz, mp /0upcelerationwu ,)/oe/(mgr0 y bpzp

  A soccer ball is kicked with a velocity of 25 m/s at an ang5c f,gbmjiqof j (7bm ql40d;1le 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-parallel tqs *.q wgxt*kmwaw9nf*mm93g94jt( ho the velocity9gwj9kmqwg*a x *ht nmq m9tf*4.3(sw vector,

  If the acceleration of an object is always directed perpendicudv6ed6h skej (00-ckslar to its velocity,6skhdjd 6s ee(0-0v kc

  At what angle should a water-gun be aimed in order for the water to land w m9.f.- id -vnvnav8iwith the greatest hor mavi.n vwnd-f9- vi.8izontal range?

  An Olympic athlete throws a javelin at four different angles abo.8ubss3.zj yp ve the horizontal, each with the same 8 y.sz .bupjs3speed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for thxtzqs /kl +stq+zv:t rn0, l64e second time. If the ball leaves your hand with twice the 0nt:, 6 qt4z+x l+slsvkt/qzrvelocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed 7bzgwx vk51.z 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 heigzn74nr0p*o mzht, how does its speed compar4 o 0rmnz*p7zne to its initial speed?

  A stone is thrown horizontally from the top of a tower ag +nv7myv6xk. t the same instant a ball is dropped vertically. Which object is traveling faster when it hits t6mxg+7.vvk yn he level ground below?

  A bullet is fired horizontally, and at the same instant a second bull 4l +- gibspw+*z c0sqfing:,det is dropped from the s nwd+psbc *z4 -,glgsf0ii+:q ame height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 72.7 m/s and at an elevation of qg: vh m;el8h8)kvfu b *y90sl238 m drops a*vs0;vue8l ghkhqfy9mb l): 8 package. 5.7 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 a plane, and one sec)op-py :8ouruond later a second package is dropped. Neglecting air resistance, the distance between the fallip:uo r8p) -ouyng packages will

  A pilot drops a bomb from a plane flying horizontall ptf:bi* f2*eqy at a constant speed. Neglecting air resistance, when the bomb hits the ground theebpf * q*i:f2t horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of th*v2 : iwk:+ og65nupfh sfgj5oat on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, th5 no6ogwhi*sku :f+g5p2 j:fv e ball would land

  You are traveling at 55 mi/h in the +x a ;fv. *8jt;ipoioh1f vxis relative to a straight, level road and pass a car traveling at fv;.j pvfi*1;h 8ooi t45 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 a5+9 zuueda2nsta 65qh;1jqdd strong current. You start out in your motorboat on the east bank desi1ha5; dnaqze+6td qj9u 2sud5ring 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 still water. How mucfcuj*7v) l w0x apas-5h time will it take you to m* 0aj-5 7csvxlfuwpa)ove 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude ;u-as3lf6b(3sm ) ri vsi+lzc8.0 m at an angle of 30 degrees below the +x axis. The y+rss6 3v(l;b lf)aizcim3u- s component of A is

  If a ball is thrown withrdj.c(wwp9us wm,:( x a velocity 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 stzdwssj -, 0tgccv;4p ,raight line in a direction north of east and you end up 2.0 km north and several kilometers east. How ts;s,4,d- cz pvgjw c0many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity is 8q;i fxy ;hl6xc 4:zrj2.00 m/s. The anglejhiq f6czrx4; l;:2xy between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long sha nzml cj as;ber1u(zc-/u7:3t dow over a level ground. At what angle is the Sun eleva muszncc/(7-3z1jaul : ;rtbe ted above the horizon?

  Two vectors A and B have components (0, 1) and ( 3lwf 8u)f15 7-s6o2nas hj.nu ggaydt-1, 3), respectively. What are the components of the sum of the 5g n2nto.8gjud7wl fss1 af6y- au3)hse two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respects zk2+v.f7i4orpl7(/hm 3 q wvc cfyqmoma- *3ively. What is magnitude of the fzq3/mc al*cfsr o(vk4m3 .m2hy-p7q o 7iv +wsum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C x i5, ggrn *v3wi .s6-ry6inqw= A + B . What is the magnitude ofyr*5rin, i-66q . ggwin3sxw v C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disp,4b8pmgrv9iyvg(s3ui 7 q1 xblax8 p(bm41gvgr,s u7qv b39 iiycement?

  Three vectors, expreyb s+baq7t p4lxk1p - t xfq1bi3hl+-4ssed in Cartesian 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)vixuemd68 k6 6aveo 3 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 pg./*:zhumpg nvkwsan)6j) 0magnitude of vector C = A/: )z.n* upp 0ghvamk6wsn gj) - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the dw 9d8(r6jktt visplacement of 6vt8 (wd9jkr tthe jogger?

  Two forces are acting onqf6 7wp1x vl.c an object as shown in Fig. below. What is the magnitudewcvqxl.f76 1 p of the resultant force?

  Two forces are acting on an object as shown in Fig. beuku73p p z5.a+.fwumxlow. What is the direction of the resupwa.+.up53z7fx mku u ltant force?

  Vector A is 5.3 cm long and points along the positive x axis. Vector B if34dm/ ofe6 (wm mpsu7h)whc* s 8.7 cmc sfmw 4pu*ho 6wmd( )he37f/m long and points at $+36^{\circ}$ 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 51 cm long and points (tb/nl7 fyqd0 at $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 42 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 sp6q6f14hpv po b tmi7m;g tc+:meed of 11 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 t:m46hqtp6 pbcm71+; vfigom to be 3.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a viu+z (sfz( zhueh 4cge jg72)5elocity of 19 m/s, from a bridge. It falls 28 m to the water below. cghieu5z2(z fh)es(+ 74zu jg How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m above the ground, strikes 5/hq8ee2g.vvb/lb x rthe ground after traveling horizontally a distance of 19 m. With what speed waseeq/x5 .v bl2/gr vh8b it thrown?

  A jumper in the long-jump goes into thio*n a) 2a ncsc)d2)kzjg ;dy-(,yjzc e jump with a speed of 12 m/s at an angle ,ozj2n(cndkjcayc;yi ))z g2a) *d-sof $20^{\circ}$ 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 spefhgz(0ovt-w ; ed of 11 m/s at an angle wtfzh(0vo g -;of $36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of jt7,eu+x4b/ 3 d3/ ei/oucfaog7 phrg 46.3 m/s at an angle of $35.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocit 8a7y 1r*jedslks3qcjxq6+x* y of 24.8 m/s at an angle of $35.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of bx:zn.zu)ipb y1nw *9 2 b1cyaj)*pgw$30^{\circ}$ 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 19u4z wt vr*x.)p.5 $m/s$ from the roof of a building 39.9 $m$ 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 ground level with an initial speed of 56.7 mn a srs z;:y-camx.3e4/s at an angl4:xsanz .; -3ys aecrme of $41.6^{\circ}$ 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 c1j gjn1uayuqc,1ku0ejm-* 2 e an 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 slows your speed by 2.1*eg1 ku 1uaq0yc-m jjneuj,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 wind of 8b z j4-h 2cyq80npzmp50.0 m/s to the Wes4byp8c2m pn8hj0 z-zqt. The plane's speed relative to the ground is

  A plane is flying due Sou0vz 1qwm0enw 2th ($270^{\circ}$) 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 ecq,u 8(wgxa+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 m/s horizontally fires a projectile with spe0qvbp 19-wd 0eq c:ngyed 50.0 m/s in a forward diy1q:0 wd gpq9-c0v benrection $30.0^{\circ}$ 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 across a river 5 w wg1s:k-q; aasceavtmt7:*with a current of 6.0 m/s. What is the speed of the boat as it crosse:7 waag1 e*k-ms :s;waqt vct5s the river?

  The driver of a motorboat that can move at 17 q/br+* ua9lid ;tnk/-mndw:vm/s in still water wishes to travel directly across a river 1.1 km wide in which the current fk a+wi tq ulvbrd9/;/n*-dnm:lows at 6.9 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 wat;j/llk xy;4 o,e miu4ter wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. Ak l4x ,/yo4mi;luejt; t what angle upstream should the driver head the boat?

  A swimmer heading direclb8h bf.;nkd/au27j ttly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m j.hud ;8t/bfn7 kbla2. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the oppositju.czghgp-y o0-s+d i+e o*n.e bank in 6 min 40 s. She is swep .u- gscoe*p0.hny+ ozd-+i jgt downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.3ljt3+(xgd jgwg9;rn 2ht08 nr 4r- qcb5 m/s, must aim upstream at an angle of 43db+r;rggq0nhtcj ln-tx jw( 89gr2$17.1^{\circ}$ (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)  $m/s$