Which one of the following is an example of a vector qi (dc37/c jnli2x;9 irf tllzn+ 4hej9uantity?

  Which of the following operations will not ch9k:h0cby+ )70m1 yh oilbt) fe lol1mhange a vector?

  Which of the followit3z37t,ss6 h .v kdkorng is an accurate statement?

  The resultant of two vectors is the smallest when the angle b:laauw aepyc4( a6w89etween them is

  Two displacement vectors have magnitudes of 5.kcl,vii60 : n8zgy1tqz iop6:0 m and 7.0 m, respectively. When these two vectors are added, the magni:ikvzpcz,80l:on6 gtqy6 ii1 tude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which ut hkc8g) 2,w:ehqus74z tar 9one of the following is a possible answer forqe7tuczh 98 gh4)a,:st wk 2ur the magnitude of the resultant?

  Three forces, each hav0 oc1s/vgedc0ing a magnitude of 30 N, pull on an object in directions that ar eg1o0d0c /svce $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkz4jxgc7tgv u l1q tf p*81+i5qnown vector is

  Ignoring air resistance, the horizontal comnsi 7g63h vfg+ponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at kzi:o,g*f*1 mi2c p zfan 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 compone mvv4 yvpm11*knt of a projectile's acceleration*4vm v1 mky1pv

  A soccer ball is kicked with a velocity of 2ka6cssl n (sckygt4 19e8-xi75 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 vecay).dr j24wdq6c d0 p:im ,zsktor of an object is directed anti-parallel to the velocity z:2pa skd0r.qd 4mc6jiydw, ) vector,

  If the acceleration of an object is always directed perpendicular tpca)):j agc/p g*vz2e g6l7bfo its velocity,bg:2pcga) )p cfgve6lj7*/ za

  At what angle should a water-gu.(xna )4ia,8 vs py5mv6kgblw n be aimed in order for the water to land with the greatest4()xgns iy6pva.85v,l awk bm horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizontba v87y 02ovdtal, each with the sava8 7o2b 0vdytme 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 for7yx uk8 u(3bko kzyt8; the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first servukx8 3kbuy78 tyok;z( e) would be

  A ball is thrown at an original speed of 8.0 m/8: cs 7swm*zmys 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 attemptu)wmmwwx6fya m,/f/3r z1p 7k reaches its maximum height, how does its speed cw m/mr3pk/1w)fwzm yuf6a,x 7ompare to its initial speed?

  A stone is thrown horpp;ft tx;6e/w*0pqo* qk q1 g9zb,xftizontally from the top of a tower at the same instant a ball is droppx, xpzqftft;go qq6w1k p*/pte9;*b 0ed vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same inh40vtjk z +,vistant a second bullet is dropped from the same height. Ignovjt0 ,zi+h 4vkre air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 58.0 m/s and+tqc1u ip*6fm)2 x4wun) tm vy7gklt0 at an elevation of 293 m drops a package. 3.4 seconds later it drops a second package. How far apart will tu 6mtvtpq0uf mik1cw*2g4)nlt)x+y 7 he two packages land on the ground?

  A package of supplies ikh+)q*0+nq6a eu 2xdexr;ed bs dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the faln;kxer dxe6*)h0q +2bu+dea qling packages will

  A pilot drops a bomb from a planea+tbqen31e+ 8j. npth l8/s oi)u ss-s flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of t e+u8e hjnt s13pl+t8 bs.qas/in-)oshe plane will

  The acceleration of gravity on the Morm1 m:f q .qy:c0x+s(vmkfq2 6ycc g*d0ngzp4on is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and ang z:mf .q (0m2cc0g x 1rgq4vqnm cdpfs*ky6y+:le) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a sticp4ac5, :wpfh(6o k8q(wjjfvyi;y+ raight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to th((j pao;k8v iwwfj4 cqph cy 5+6yfi,:e other car is

  You are trying to cross a river tha;0d4js :,udasra3e kz t 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 should head your moto:da er4uks;,js3zd0a rboat

  Your motorboat can m,ufo8 *; fa ifmb:1rvzove at 30 km/h in still water. How much time will it take you to move 12 km dow8:f;fum za i, fovbr*1nstream, in a river flowing at 6.0 km/h?

  Vector A has magnitudvn1dfi6o 8fdlgs:( e/e 8.0 m at an angle of 30 degrees below the +x axis. The y component of :n fd1s6dgl/f( i8ove A is

  If a ball is thrown with a velocity of regc3.4b q,k x25 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 yo9wr;5 x .r-39gfu d)8nlliixn0c ab flu end up 2.0 km db8xwx9fl. 5g3 il l 0; f-ar)rcni9nunorth and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component ofhb/: kpxv v44i its velocity is 8.00 m/s. The angle between the directi/kbivpv4 hx4:on of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level grounj06 f7*txi1ci uuu pax o (d:,+.enjt-okc g1od. At what angle is the Sun elevated above the horizo uc*t o-17c( utd+ige 1 ,0okfaixjxjn6.po:un?

  Two vectors A and B have components (0k : ttj:sqbb 8a3x( zq/s(vgy*, 1) and (-1, 3), respectively. What are the components of the sum of these two vecza3kty*( vbx:sqqg /st 8(jb :tors?

  Two vectors A and B have1-kws0 we ix0s components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two ves0 eiskx1-w0w ctors?

  Vector A = (1, 3). Vector B = (3, 080)rkupq*hdxij. ep g a:0x1o). Vector C = A + B . What is the magnitude u18).jo pqh0axir0 dpek*:x gof C ?

  A car travels 20 km West, then 20 km South. What./3 l lcp(ed49-wb:efsi glo t5lf .hy is the magnitude of its displacemenc to3eghpi9ll54lybff / e.wsl-.(:dt?

  Three vectors, expressed in Car1ea4szmdz9uw// ;ukntesian 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 coordinates,wfw;m an7d0p cvf(t6 e+ ;qb,v 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, -bf, g ;qp)-ndj4.0) and vector B = (+3.0, -8.0), what is the magnitude ofn,bg; qfd-jp ) vector C = A - B ?

  A runner runs halfway arougjk4frr lry,, 3q 3*yvnd a circular path of radius 10 m. What is the displa,33yr lg ,rqyj4fk*vr cement of the jogger?

  Two forces are acting on an object as shown in Fig. below.xel-; ryzbi- g0wrgg*1 4u.u i9iy+dy What is the magnitude- 4ueibr0w91ii .yg uxydrg- *zy+gl; of the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the directisn+ 2wpb4f) t7*z+k8wdt3t jtc6br fur1jei1on o7j1wsn4 w) it8rdpr3kt 1+z ft+6jbc*tefbu2 f the resultant force?

  Vector A is 3.5 cm long and points along the positi ,/:d9 *; l;ysrqw9 ffssnhcndve x axis. Vector B is 7.2 cm long and dwyc: s*r 9nn/ fsf9;q,dlh s;points at $+40^{\circ}$ 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 poavt v5 z10oqa9e2nhxu ww) )t3ints at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 31 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 snn+23/n bf myepeed of 25 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from tn3b+ 2nmne y/fhe top of the cliff to the bottom to be 3.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 7 m/s, from a bridge. It 6wup+crvi ; jz2h 1q6bfalls 26 m to the water below. How far does the rock travel horizontal62hcp iu6+q wvb1j rz;ly before striking the water?

  A ball thrown horizontally from a poinw m-f, yr, ,lo1-az go8reex))p7ntvwt 27 m above the ground, strikes the ground aftgtw por xwr7fnml,- e-,8a ov1 y,))zeer traveling horizontally a distance of 14 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jumya41qm qknz. /z mc.*op with a speed of 12 m/s at an angle ofqz. mz/nak qc41oym.* $20^{\circ}$ 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 11 lgu) zve ie:oxkio55w 74g3lw hm,c2+m/s at an angle of )mig:cg u+74vhw55ke 2ozx ,w eol 3li$37^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 27.8 m/s aewf7r *p y,dw8t an angle of $37.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 21.2 m/s at an anglq,dd a n5 0i,l ms;(aat+lsib5;gy8wq e of $23.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at,231mzxj3hu bib)b k f an angle 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 horizontall4u s3j5 yokdh;y at 20.2 $m/s$ from the roof of a building 62.8 $m$ 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 wigwu xppw.ot+8 fk bby9-6b5 x*th an initial speed of 56.4 m/s at an 5p.9xbwkfy u-tbg+b 6xo w8 *pangle of $45.2^{\circ}$ 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 run a 1500-m race at a velocity of 4.0 m/s. b6a1(yrbrf9b If you ran the same racbb6 9(1bafry re on a day when you had a constant headwind which 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, and is in a wind of 50.0 m/suxmpk kgg9fh(3 ezy42qcp3 31 to the West. The plane's speed 34u9myqgk1k pe33ch (z g2xpfrelative to the ground is

  A plane is flying due n r p) x*kaas-d/s:ndjn .21plSouth ($270^{\circ}$) 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 u;e az2xg3ajjt92t-( 8fqgp m**di ka 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 mm:-2sgwv 0c ns/s horizontally fires a projectile with speed 50.0 m/s in a forward di: vnw- 0mcgs2srection $30.0^{\circ}$ 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 watehb jc.s:,l ,ker is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crossels,ebkj. c:h,s the river?

  The driver of a motorboat that can move at 15 m/s in still water wisheljwo sb6l8x:a0i), ),z4s( esnp nvres to travel directly across a river 0.7 km wide i 6 e,vxbn)4si,s0ewzo( s)8lnjl apr: n which the current flows at 6.2 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 s*jb)*y(hv /sxieeo 2water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle (ij*esv/bx2soeh )y* upstream should the driver head the boat?

  A swimmer heading directly across aq(ahv p(h 7z9r88qt fn river 200 m wide reaches the opposite bank in 6 min 40 s. She hq(p 89v(af7qzh n8tris swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide r+wa 6nvnpi b*3eaches the opposite bank in 6 miabn v+p* wi36nn 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still waterii(fm+x 3bocr7f8r9w is 1.03 m/s, must aim upstream at an angle of w+bf 8cfmroi x73r (9i$31.8^{\circ}$ (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)  $m/s$