Which one of the fol,u 2:fdnb qc5c.zy0t 7 ng zi/u90xaytlowing is an example of a vector quantity?

  Which of the following operations will not chans,6pi4 pz.qg kge a vector?

  Which of the following is an accurate s:a kk4i2i-vw itatement?

  The resultant of two vectors is the shhys;z+ioe /9vbqt8.uew *;4f qoop5mallest when the angle between them is

  Two displacement vec ,x7xkkrxfou -p 5u-0htors have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors auuox ,fr5-p7 k-h0xkxre added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one rx/-u+kg m0v9 l4qnrv(h5um zof the following is a possible answer for t-vr l q04g /+umxmuhnrvz5k( 9he magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions vx,)rijrq az9kvc 4 /:that, a4/rrv 9i)c kxzjvq: are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector ic;ynuhjo 1 ucr11:ow.a-g m9xs

  Ignoring air resistance, the horizontal component of a projectile's la.:nzx613-lz2ekjqqq /6mxvxf*rw velocity

  A ball is thrown with a velocity of 20 m/s at an q;rhjl8uk9e3 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 proje lnc cmcu 6h8nm 2wds78xb3+p-ctile's accelerationxh7l c8+w bnc dsu8ncm-m3p26

  A soccer ball is kicked with a velocity of 25 czuo9hb18 z/em/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 directed anti-parallel to8c:ze d7e53v p.t1pial9*mt sqjt y)r the velocity vectortt5iam9 vetlqej3:7c1 z* rsp.pdy8 ),

  If the acceleration of an object is always directed perpendicular to b: s1c1;va/(q xczyi dits velocitx; cvy/a:zqbd( s c11iy,

  At what angle should a water-gun be aimed in order f we1qp* .lwr i) xih6gjmn3i*0or the water to land with the g*w m3qlg6i *ixjni 1p0w. hr)ereatest horizontal range?

  An Olympic athlete thwdz0bml *qb qcl - b:3pgv.jf(*k8c v+rows a javelin at four different angles above the horizontal, eacb bjqc3klgv8 -f*l( wzqb*+pv :.m0d ch 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 the ball leaves+ n0t0f .qof6mew*h3xqw( hhi your hand with twice the velocity it had on your first throw, its horizontal range R (compared toq+ 6wmi(he 0qf ht 3xw*fhn0.o your first serve) would be

  A ball is thrown at an originalv) . ounc+:gqc ysd/y)xv, kf, 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 attempt reaches its maximum height, how does im f hv217(dcf:)y vztnts speed tf2 c(vz :dnv)mf 71hycompare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant 3(f21b astmlka ball is dropped vertically. Which object is traveling2 mb(s ta3f1kl faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet 8z/r jxvzoyvz.(/e0pue 6vv/ is dropped from the same height. Ignore air resistance. Compare the ti/v vz6px.er 8vj/0zuz (oy/ve mes of fall of the two bullets.

  A plane flying horizontally at a spesh3 i3v1gc,y01bxr jra; ;qytz6,ekded of 64.6 m/s and at an elevation of 147 m drops a package. 7.8 seconds later it drops a second package. How far apart will the two pax1h a0kiqs cge1brd j,;z ;v63rty3y,ckages land on the ground?

  A package of supplies is dropped 5a)c5;di4rk1e w/ e6;igtptfx(- ngu 0pudccfrom a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packge4n pawf ;c6u0 c5xkeipud;t(t-1 icd)r/g 5 ages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. f s:ro *a.1o59 8utwre6cxqihNeglecting air resistance, when the b6x8fsc *u oworiah t q19:5.reomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. z d +/v2qwctggw*7jnz3 boq2 9 If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would l+d 9qcgvojq7tb322z *n /wgz wand

  You are traveling at 55 mi/h in the +x axis relative to a straigo,wcpz;: zatnzm-v6 . ht, level road and pass a car travotap6n-mcv zz z., w;:eling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows 1g96iq ablha0.5vlblyw 7ht - due south with a strong current. You start out in your motorboat on the east bank desiring to reach the wal-79 v1t 5iah lbh60b g.wlyqest bank directly west from your starting point. You should head your motorboat

  Your motorboat can m6inb+bs 4q+u ;uzj85exom96 xq5uekuove at 30 km/h in still water. How much time will it take you to move 12 km downsq+bu66izx9 u5qk exu 5;+ e48jsnoumbtream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle w e bmctg+y:r 2mhfe74i1e2q1of 30 degrees below the +x axis. The y component of e2cbrm y4weg2 iemqf:+11h7 t A is

  If a ball is thrown with a velocity of 25 m/s at an ang*hqbsy :10xibnt7c* dle 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 m1 b qm: eb,e4k;uvo-yu7rzpzr67t h6east and you end up;k b e77qrpyuh:1e6o umzb,rmzt-v6 4 2.0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 jew/ +6cvksk6m/s. The x component of its velocity is 8.00 m/s. The angle between the dircwv/+e 6sj6kk ection of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. A a9akam v5h/s;ascw(5t what angle is the Sun elevated above the hork mv/5 w 9shaaa5a(cs;izon?

  Two vectors A and B have compob4hih ji8g3.l 3ftw 2rnents (0, 1) and (-1, 3), respectively. What are the components of the sum of these two4. 8wtl ri2ghhb3ji 3f vectors?

  Two vectors A and B have compong80wg jeldjg kq84a:,4qh3gi ents (0, 1) and (-1, 3), respectively. What is magnijgkg 8il: e 0 ha38g44j,qgqwdtude of the sum of these two vectors?

  Vector A = (1, 3). Vectort,g4dn-k nxtugh;t q*(h : 9tr B = (3, 0). Vector C = A + B . What is the magnitude ofrk(x,-hgttg tun;qt :hd9n4* C ?

  A car travels 20 km West, then 20 km South. What is the 0du*q+. pzes0 7aq (za/:p-ztl gnbrmmagnitude of its displacemea( nsdq 0 /rzbq0:.p7m t*z g-epl+auznt?

  Three vectors, expressed in Cartesian coordinatpi o :(6kz s9g*nbtx-qes, 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 C9q:lou xmbcij s; z8+dew .+zbo(,:nk artesian 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 odd+w h5+c q)ethe magnitude ofcd+5)dheqow + vector C = A - B ?

  A runner runs halfway around k6cg) ; ;n b 1.ik;jj)9jt3npoyzsgv ;;qlhpva circular path of radius 10 m. What is the displacement of the jgkl;hn y.og61 jcqtpibnzps;v; 3 j) ;jv; k)9ogger?

  Two forces are acting on an object as shown in Fig. belz-5fa 7 p5e2+ ogcmyscow. What is the magnitude of thea c-+55spy2fogmz ce7 resultant force?

  Two forces are acting on an objedit72gl glw88 ct as shown in Fig. below. What is the direction of lwtl g27 i88dgthe resultant force?

  Vector A is 3.2 cm long and points along the pos ,f; kv+w pr-j3l pb-q(jdqce9itive x axis. Vector B is 6.2 cm long and -d( wce v,;-r+pbfq9jlkp3j qpoints at $+30^{\circ}$ 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 60 cm long and /e4b ,caz hf5gpoints at $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 33 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 2nohal:c zp)t3+l2a1 m 3 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 bol3m2l1taca)zh :op +n ttom to be 3.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a bridge. Ihlq3ooyt; e8v 83qj6wi(p ko;t falls 14 m to the water below. How far does the rock travel horizontally btqh jk6 ypo8qovl833;; (iwo eefore striking the water?

  A ball thrown horizontally from a ;qnfc.;j/ ao7qx7 ( keb6 lqucpoint 25 m above the ground, strikes the ground after traveling horizontally a distance of 23 m. With what s;7(lu.kcqj/a6 necbo q; xfq7 peed was it thrown?

  A jumper in the long-jump goesk9zac6wv 3e)b/wjtg+ into the jump with a speed of 12 m/s at an angle ofjc6w /3wkzevgb9) ta+ $20^{\circ}$ 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 bus 9k 3onnpns/yy76/speed of 10 m/s at an angle ony/yk3 su9on p s67n/bf $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity okg-pw 43(r:hwj atepq.5vw r- f 56.6 m/s at an angle of $38.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 38.9 m/mrz i ,k+4ra2*h h:agys at an angle of $36.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle 8lrb9 wc c6(ujof $30^{\circ}$ 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 ak rco2z;zf+df ;6(rsut 17.2 $m/s$ from the roof of a building 33.9 $m$ 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 spelm;zs/0ow 9qv2ce w4ned of 57.3 m/s at an a 2o/nswm49 cvz ;w0qelngle of $38.4^{\circ}$ 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 winoz mz 89h 1zu 3h2l2zy,)rquzld), you can run a 1500-m race at a velocity of 4.0 m/s. If you ranh1 z98mr,lz yzq uzuz3)ho2l2 the same race 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 sfnjlr c+5c1v lo)ih:dk1;*ml 6/uksfpeed of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speedf*6k+kclc u1hli/m ; j sln5dorfv: 1) relative to the ground is

  A plane is flying due Sout;.b)w9usf;mj gat ib) h ($270^{\circ}$) 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 headedlpik (kn k.3:w $30.0^{\circ}$ 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 c.z sjd(u0voc )b,ug4projectile with speed 50.0 m/s in a forward ucu)vjdgs (.0b,zc4o 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 wx4e)sr6ew/ qb/8gfl/x8w qb l ater is 8.0 m/s, is directed across a river with a current of 6.0 gw)qbx// qfxl4eelw88br/s6 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in still water wishes ( 7)kp idn7-qwh2flrp to travel directly across a river 1.8 km wide in which the current fl)(ih r lp7kdw7-p2fnqows at 7.0 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 u ka 9nf a:fzjw0u3b5.z-par ;water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angl.j0- pzwf n3a;zkraf9:ubu5 ae upstream should the driver head the boat?

  A swimmer heading directly across a river wi*jflhu/v :-200 m wide reaches the opposite bank in 6 minh: il*wu/ vj-f 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite 1poe57nstg.m bank in 6 min 40 s. She is swepmps15 og .et7nt downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.27 m/s, must aim upstre3 iwobe .epj y 0:cx2g6x+n* 3bevk8eoam at an angle ofb0xx.ivn 3 oy3 gk2op+ew8 6:jbec* ee $19.3^{\circ}$ (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)  $m/s$