Which one of the followvl2serktw3b+ +u x(0 cing is an example of a vector quantity?

  Which of the following operations will not changcn 2hill*t, c3o9v7nge a vector?

  Which of the following is an accuz .c+u4ck;y )w; bul/unscf4yrate statement?

  The resultant of two vectors is the sm73 faz r)a*z1f/aq) aoosx6dpallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. Wh (gcb: pih6,mten these two vectors are added, the magit m, c(hgp6:bnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which onx n ;- 5exaue9;pi 1d.fjhrv:qe of the following is a possible answer for the magnitude of the rjf ;ph-x a :.51vrexqei;u dn9esultant?

  Three forces, each having a magnitude of 30 N, l(ga js)-4ay qpull on an object in directions that are(j -)l4qy agsa $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the 3 ,t p+xjun:zztmd 4o;unknown vector is

  Ignoring air resistance, the horizontal component of .ks .hk-il: pea projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle fwi/xm )w:)5xhri.v-iz2 exxr i(zi. 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 horizontalteu yt 1lu) r bfcyd/arg,;2*( component of a projectile's accelerationr(b ;uu* ,dfce/tal1)ry2 tyg

  A soccer ball is kicked with a velocity of 25 m/s at an angle of p)(,fujcqf2 m$45^{\circ}$ 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-parallele-/b yz*icfcbnj 0 ;+r to the velocity vector, b f;r i/+zyce-c0njb*

  If the acceleration of an object is always directed pa1am3 /l/b9n wftc 9raerpendicular to its velocitya 9 n/taa 3wf1m/lrcb9,

  At what angle should a water-gun bbr xz,m, k;jt+h5do8i e aimed in order for the water to land with the greatest horizxzkhm ;o +bjtrd58,,i ontal range?

  An Olympic athlete throws a javelin at four different angl1 eb+en2by5r)3i 2ti dgi0pbues above the horizontal, each with ti5b b2) y+gt 3be0rip1ud2neihe 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 secoh8r 6uba n4c1knd time. If the ball leaves your hand with twice the velocib4r1uha kn8c6ty it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an origncu o) mz2w)grju i66*inal speed 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 ax+4nm m hr:,:l z:lonmn+l2qpttempt reaches its maximum height, how does its speed compare xl2+lm n :+,l roq:mmhp :n4nzto its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instantxgf /h8 t1/0rbq,xo7mhcds j 1q05ny r a ball is dropped vertically. Which object is traveling faster when it h,bgy q87q/ omhndfrx cj r050t1/1xsh its the level ground below?

  A bullet is fired horizontally, and at thebkwb0x3uk) w6- zzl ,m4s:ih iwo0 y0q same instant a second bullet is dropped from the same height. Igni s- z 0:00 zqm)kwbh,wo k463uxibylwore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizonuftnjg:7l3 4 nhlt r*5tally at a speed of 116.6 m/s and at an elevation of 165 m drops a package. 5.7 seconds later it drops a second package. How far af5g7* : 34luttnr jnlhpart will the two packages land on the ground?

  A package of supplies is dropped from a pdm wcm zyteik2b-x k5*9vqe iy ;3+-8clane, and one second later a second package is dropped. Neglecting air resistance, the diez*2iyq;3dm i8t- v -kwy+ bcmck9e5xstance between the falling packages will

  A pilot drops a bomb from a plane flyizsd kh k2o+nr)2gh 3)qng horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane w2n 3skg ))dkhh rzo+2qill

  The acceleration of gravity on the Moon is only one-sixth o+g0 t:b1 y-k+lr 8kp9hwq4ldg pate9q4 oc3cpf that on Earth. If you hit a baseball on the Moon with the saplc+qg9: 4t0 dkkar4e 9- pg1olty+83c bhwqpme effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 miba w8;79ie2 s7:r8asaxenc xs/h in the +x axis relative to a straight, level road and pass a car te8wnaa7e ; 2bxa s7xs:rcs8 9iraveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to crop82 lix s2;qjrss a 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 from your starting point. You s s;lx2p 8jqi2rhould head your motorboat

  Your motorboat can move at 30 km/h in still wate xe2pryb7j.q;r. How much time will it take you to move 12 km downstreamq7;pre2bx .yj, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle2/(z q0 rase39tnn,hway/b ef of 30 degrees below the +x axis. The y compo/n/na(,ftw2hzeey r q 3 b90sanent of A is

  If a ball is thrown with a velocityhvg 1 nx9,skth.pd 9o4i;; phn 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 strb,t s1f7*ci xyaight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have youy 7*,b xftic1s walked?

  A butterfly moves with a speedeu y,ou,6(as( djhxl ) of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion ansj6 (d,yex l(,hau)uod the x axis must be

  A 400-m tall tower casts a 600-m long shafirx5k6 /ogp03 b36t j;eywj xdow over a level ground. At what angle is the Sun elevated abo ;3ke3b/tx65xr 6fpgjjwi 0 oyve the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), resmojbek i5su m1:/,d9x* oc5d dpectively. What are the compondd5 mmo *, 9 u1kboic/:5xjsdeents of the sum of these two vectors?

  Two vectors A and B have 31t kaa6sppey,3*y*sh j, 8pe; djstz components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these tpeyt6ks,y;hd 8 pj33*as1,satejz p * wo vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vec-ml:z1t l6nibh-8c fjtor C = A + B . What is the magnitude of Cc1h8n-6j :mzlf lit- b ?

  A car travels 20 km West,m6n-e a, ws /m(ql0o p7uot(vu then 20 km South. What is the magnitude of its displacementau- w o70sl uv ,pmo6en(q(/tm?

  Three vectors, expressed in Cartesian coordinates j+ 5s ph bag7j0;fbdsdsy0s4*qcm95h, 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 ylzfoz)z5v + 7coordinates, 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 = (ifkct ;.dixul;9p+z 4 +3.0, -8.0), what is the magnitude of vector C = A - B dpxk;9t4ci ;i.fl uz+ ?

  A runner runs halfway around a ciu7c5 lv wlu o,l6eg+y+uh7hm +rcular path of radius 10 m. What is the displacou++ wcvu l7g y,l7lme +u6hh5ement of the jogger?

  Two forces are actingcdkf8 7wp oa9 l a8d:bl+/:e0sglsa9q on an object as shown in Fig. below. What is the magnitude od od9 ps:lg7 0qeasaa8kbl/:98 cw+fl f the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the direphr4x 6 fxp (xjf,u70ection of thxf, xe0rxph46 juf(p 7e resultant force?

  Vector A is 3.2 cm long and poi;;*is+xiff x, u0tyni4e, fuhnts along the positive x axis. Vector B is 7.5 cux +;iff e, *;4ixiuy0hn,ft sm long and points at $+59^{\circ}$ 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 80 cm long and p3r(uo :kmf,sqvdi*f 6 oints at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 29 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 20 m/s from the edgemce) jxx,suo k2v5;0f of a c5 cux) m 0,vef;oxk2jsliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with at61j1 i1qt jbm0r yif/ velocity of 10 m/s, from a bridge. It falls 11 m to the water below. How far do0ytjjtf6 q1 ii br11m/es the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 26 m above the ground, strikecz:md/; dgvzp xy+4v72 )kzyls the ground after traveling horiv;z4 : cdxg7)zp k+ldyv/m 2zyzontally a distance of 14 m. With what speed was it thrown?

  A jumper in the long-jump goes into the atq )iot;819bwx y n(s+qzt q9jump with a speed of 12 m/s at an angle of 1awq;98ni tbxo qyq )s+(z9tt$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into th jn5mb4- p/plogre 8+ce jump with a speed of 11 m/s at an angle o-8 bnlmrc5op g+ej4 /pf $38^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched wid:*a lqk. 6zfa)ip b 5(za9gvvth an initial velocity of 35.1 m/s at an angle of $12.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched a g-vbo0 my6+ 5bgjf8swith an initial velocity of 24.8 m/s at an angle of $43.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anv5wmvkyar 7qlm ;y1/7gle 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 )wj6 -wry-xoj.sc yo3at 23.0 $m/s$ from the roof of a building 69.1 $m$ 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 grocksi4b +;9 mgaund level with an initial speed of 47.2 m/s at an angle a4c;bg+ km9 isof $42.1^{\circ}$ 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 1500-m race at a velol+(;+m totron 5bie jpne+ v4;city of 4.0 m/s. If you ran the same race on a day when you had a constant headwind wh oe+; v4;nl5tor(mjn+e itpb+ich slows 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, andki) ,/ou ;pe oyi(m7n-hi.hoo is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground iky.ie h o uiph),(7oo o/n;-mis

  A plane is flying due Souzov yx r68hz u5,wm,0uth ($270^{\circ}$) 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 e9/ w)kbzc6 apof 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 m/s ho1nx8 )e,mrkdt0t-s.x w dmhp0rizontally fires a projectile with speed 50.0 m/s in a forward directie 0xt,td 0xnr8 s-)1.khmpmdwon $30.0^{\circ}$ 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 wat9 aiison/:s+nn t u zt x9/1 w6q7c72xb:bzynqer is 8.0 m/s, is directed across a river with a cunw/:q z9 b7qnt+yii7x s:s nun91a/ozbxc26t rrent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat t v/ap)6(sp ybphat can move at 15 m/s in still water wishes to travel directly across a river 1.1 km wide in which the cusp p6/) abvy(prrent flows at 3.1 m/s. How long will it take to cross the river?

  The driver of a motorb 8 g-mzspxbu446i 85+oeubcbzoat that can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows ate bzmiu gb4c8uz+s-xb5846po 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reachesx*oatzq j,p9-c umy4g 24)r el the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still,p 9 - umjgcy2exaqt4*r4z )ol water?

  A swimmer heading directly across a river 200 m widv fr cnt9 i5awzp1s552ik.tk* u/8irce reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the spee1.uani2k9 rip 5f5 w8s/ziccv*tr kt 5d of the current?

  A boat, whose speed in still water inlp0rl dn:2. js 1.03 m/s, must aim upstream at an angle of 20rd jll :.pnn$30.8^{\circ}$ (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)  $m/s$