Which one of the followte,j/u1xw ck+ rk+ q/ling is an example of a vector quantity?

  Which of the following operations will not changl.*,u d23rt8 usaqdyge a vector?

  Which of the following is an accurate statemena txy;5jcn g770daf+jt?

  The resultant of two vectors is the smallest when the angle between thennrs/sac )ot.v9w/-rw 9j5uam is

  Two displacement vecto pii9 (y7pzoq: .in:hirs have magnitudes of 5.0 m and 7.0 m, respectively. When qpo:9h:.p ni yii7(zithese two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and uyk+ bwl- w8tzf5z2y6 50, are added. Which one of the following is a possible answer f8bw+y2t5 zwzuf-kly 6 or the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object i0wlma,3i6r i sn directions that ar a0i3iw6,lmr se $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown 7 q-2pv.drjb ivector is

  Ignoring air resistance, the horizontal component of a projectile's vel s9tw: xxckhehh 8 6.1winzl*3ocity

  A ball is thrown with a velfc;sa1f2j6g p ocity 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 resistan,1wdrm) eo0-pwtot *rce, the horizontal component of a projectile's acceleration1or, -rt0tem* owpdw )

  A soccer ball is kicked with a velocity of 25 m/s at qoke nk53wp 4yj 6nnp4ek. -v/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 i6qxuk bvv gwc+n -gm7t;9qx 31s directed anti-parallel to the velocity vector+xxn6wq -t31g vvgmk 9bqu7 ;c,

  If the acceleration of an object r tjzt1yq)7y.is always directed perpendicular to its velocit .yqt yj7zt)1ry,

  At what angle should a water-gun be aimed in ord/ .;+a;+l- .kret o6 o,c bjx2mqw,izcjjlpc cer for the water to land with the greate l/l;,k 2j6azxwjo .c+b+ccrc. ieto;-pm j,qst horizontal range?

  An Olympic athlete throwso:6f97 sfecjh a javelin at four different angles above the horizontal, eachs7 oj9fh :cfe6 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 thepy;/o6ns +*jnfinrr7 second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizonty7n*psi o/fr6nj+; nr al range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.9yff i:gj2ysy c71sk rfs( ;e.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 4 x7n:te+r+h apccog x9px ;t5its maximum height, how does its speed compare to its i xr4hpa ++5x:og n9cet ct7xp;nitial speed?

  A stone is thrown horizontally 9e,j h7*jl08oi uu umox(g(fx9) egsxfrom the top of a tower at the same instant a ball is dropped vertically. Whicg*mxl je7uiu09os9gf) o(xe( 8uxj ,hh object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a secon *zga lru- w;wj)s5k0ae nc3s+d bullet is droppew5gs)un0- er a3 ;jk*wc +sazld from the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of c1n bp wlsgvt*co-u0l,q*7 j355.2 m/s and at an elevation of 132 m drops a package. 4.9 secon*bcv7s3u1jclg t o-l qp,wn*0ds 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 o81jxsool rw9 6ne second later a second package is dropped. Neglecting air resistance, the distance between 8oxrs91jl 6wo the falling packages will

  A pilot drops a bomb )xkglor, v(r4josw 8, from a plane flying horizontally at a constant speed. Neglectivxo()4, ,o sgr jrk8wlng air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on thedztb -rz5f/:g s9llv 0 Moon 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 angle) that you would on Earth, the ball would land0 /b:t zfr-vd59zglsl

  You are traveling at 55 mi/h in the +x axis relative to a st6.p7cpn4xq 0zgck25cw+k8u ib tq1 s,rcd u*sraight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other wnk6i *pp+q.z172bc , 4dcqcgr0tuusc8s5k xcar is

  You are trying to cross a river that flows due so iryvb 5/f8x8juth with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directlxfb/ 8y8ij rv5y west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will itr; hd6e 04 r(nay hyp5bohy8-m take you yh h4 pehb8nar-yr0(o65yd;mto move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below thepr;2ns 3lvx- e +x axis. The y compe-; s3lvrnp2xonent of A is

  If a ball is thrown with a velocity of 25 m/s at an anglefh-q(w3 hmdwcs.e*x9 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 yous0o0j6u vw9ff end up 2.0 km north and several kilometers o6ujwf9fs0 0v east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x compotjibp,ok2 7 sn3,s g7hnent of its velocity is 8.00 m/s. The angle between the direction sjnsoki7,b 7hp2 , 3tgof its motion and the x axis must be

  A 400-m tall tower cas3w sjbz tkr2m-of*rj6o7 d.+r78fw omts a 600-m long shadow over a level ground. At what angle7 db8 s6omj.r3womrf r*of-zkw+ 2jt7 is the Sun elevated above the horizon?

  Two vectors A and B have g dddz2.z g13 *l 5bgpyykr9f7components (0, 1) and (-1, 3), respectively. What are the components of the sum2.ddbrdzzgy *f pyl9g3kg 751 of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivel gb 7(lzgng09ly. What is magnitude of t9l0bglg g7zn( he sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitudqv/d8(hsxk yk hiook3we: +, /e of C+hoksqiw8/(/y ed o vh,xk:k3 ?

  A car travels 20 km West, then 20 km South. What is the magnitude w f g/rza416rrof its displacement1r/agrw6 zr4f?

  Three vectors, expressed in C1kcv/w : yxh.uartesian 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 Car: :e84 nwo5v aiyma.ettipo9,tesian 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 Bss;( f4xozjinfe 273q = (+3.0, -8.0), what is the magnitude of vector C = A - B2x njz4o7fsfi s(3 q;e ?

  A runner runs halfway around a circular path of radius 10 m. What eaafs)4av n xc.)5zc/ is the displacement of)faeac nx) 54acsz .v/ the jogger?

  Two forces are acting x+l.l rlx1v-7lw 8vkg on an object as shown in Fig. below. What is the magnitude of the vvk.g-l l8l +rxwl7x 1resultant force?

  Two forces are acting o-nlqk q6pzw9:/ ) v fi5k5jwtkn an object as shown in Fig. below. What is the directionknw v:69pi)k-5k /t5qw lzqjf of the resultant force?

  Vector A is 3.0 cm long and points along the positive x axis. Vectd .gci w)pmb d )x4l0yit97y)lor B is 9.1 cm long and py4xyip.)9lgdmi7dc 0wl )bt) oints 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 81 cm long and points at )xdzcnd u4)* 7kymbv- $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 39 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 horizontall ooiv6m .u2y(fy with an initial speed of 25 m/s from the edge of a cliff. A stop watch measures the stone's trajectory t6mu. (o2o yfivime from the top of the cliff to the bottom to be 2.1 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 17ggs29epy.g 4 h m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontgey2.9ggh s4p ally before striking the water?

  A ball thrown horizontally from a point 27 m above the gro ;8rdpinqaex3f7 m9/ound, strikes the ground aftera3mx ro7p;8q/efi9 d n traveling horizontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump;23v *fver*nf+gtxee1dce j :*q-dsl with a speed of 12 m/s at an angle of :s fc**jd-e extge v2e *qf3+;rvd1nl$20^{\circ}$ 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 8 m/s at an angmnm: at amcj18 s85nj)le of jna 81 n85)m matmcj:s$29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of ua3l6-8,g y cat az3lq38.4 m/s at an angle of $35.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initiaz x-9fak xf-vhu-is(2y6.pkk l velocity of 25.1 m/s at an angle of $38.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fiaz4oq4g r2m/ kred at 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 horizontallyt58qj7 r1f./ kozdr ny at 24.5 $m/s$ from the roof of a building 57.6 $m$ 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 l*m,xqtt im4 lyw7;bn**dd:muevel with an initial speed of 42.0 m/s at an anglmw :q;dl*x4tu7mbt* d,n*m iy e of $37.0^{\circ}$ 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 136ryyzgnv m h7)tr9za 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 2.0 m/s, the time it wouldz r3 9nvthym7 r6zy1g) take you to finish would be

  A plane has an air speed of 200 m/s due 282vma18avr0b nx en igg/ek-North, and is in a wind of 50.0 m/s to the West. The plane's speedvx 10 -2me/v i8n2baagn8rgke relative to the ground is

  A plane is flying due So/i,5i vov gz0gl +:uhwuth ($270^{\circ}$) 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*9*rtuz9yth (i 1quh d 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 20/8je fd9n zs-5w6o cpg0 m/s horizontally fires a projectile with speed 50.0 m/f9z8s dogw-65ejpn /c s in 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:gi*v eugx-f* 9wlhu, water is 8.0 m/s, is directed across a river with a currentx,hlegig*u * :9-uw fv of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can 6h zygk8p3wi) move at 18 m/s in still water wishes to travel directly across a river 0.9 km wide in which the current flows at 5.8 m/s. How long will itk )i8gzwyh 3p6 take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to tran;i s4zrej/ ihyce3::vel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should: 3y/jenii4csehrz :; the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches th ua m (0v;iiegf3r.d 9::z d9fctu0qdqe opposite bank in 6 min 40 s. She is vt3099eqi mzg: i(d.c:dfuru da 0fq;swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a rix62p 0+pj uusf7 gbg7h, dmhyh6u.w1q ver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstrp7m .g71huh60 s uw,hj2f 6qd+pyxgbueam 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.91 m/s, mustzx8h( wwtl 50z: hfcang 9r1y9pqhp1h: l 12we aim upstream at an angle of(l9q1ywfh81 rxpw gw2z 1h: pan5zlehc0 9 :ht $17.1^{\circ}$ (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)  $m/s$