Which one of the following is an example of a vector qfpzr g5:;wj 3tf01fo puantity?

  Which of the following operations will:ln y4 (v3mt+z pmb3j5sqi b1z not change a vector?

  Which of the following is an accurate 4hjfo y (c48 u-tzv+*kpw4 cuqstatement?

  The resultant of two vectors is the smallest when the anglej68 6vg40myfvn l4m yn between them is

  Two displacement vect(va+) 1a lvypfors have magnitudes of 5.0 m and 7.0 m, respectively. When these two vector1pav)al (+vfys are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are addedf ;p48gg )trv63*n6 bgaoyi.ezx 3b zk. Which one of the following is a pozxzk tgn*.b3fo 8eir)ybavg43p ;g 66ssible answer for the magnitude of the resultant?

  Three forces, each having a magnitude oc a.dk) m0lm/nf 30 N, pull on an object in directions tn)/kdmm c l0.ahat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowabvhbk.u 5g) 9n vector is

  Ignoring air resistance, the horizontal com laaet82 ;ky;cuj r. kkw8-(22zox num/:dyydponent of a projectile's velocity

  A ball is thrown with a velocgv1hni+sv5b6m l5q- j jf10ality 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 resistance, the horizontal component of 4uqdm.zpx q61/6u.ug/bf c o+*idk wn a projectile's accelerationm upc.nwiubq dxuk/q1*.dof +zg466/

  A soccer ball is kicked with a v-.8br0m lheq,j px:bxelocity of 25 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 vector of an object is directed anti-parallel to t1n 393bb xyx/v 1c cd9 0/gscul8zhtdwhe velocity vector,xb /d19c th1 ux8csny b3w/cvgz39l0 d

  If the acceleration of an object is always directed perpendicular to its veloci6fna5oafaxw( 6rf+u2 ty,nwf66 (f +rfa5xou2aa

  At what angle should a water-gun be aimed in order for themj9 . gjgj v/ffe-42ht water to land with the 4fthjfjj9-ge g /.2mvgreatest horizontal range?

  An Olympic athlete throws a javelin at four different ang3j .tb c7x:cl tr6*6-rpxmk klles above the horizontal, each with the sam*.-3rbxl6m jt:r xpt c6ckl7ke 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 leao)i(pkm6 -i nfves your hand with twice the velocity itmfn-(6 io)i pk had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original sr s*.z*-g m)scx:fesej3qqc g (x7n4zpeed 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 maxim*z2h6; :b) vsm8of c+eqd rfvxum height, how does its speed compare to itsdq)v*2osxzmh e+rf 8;6:v bc f initial speed?

  A stone is thrown horizontallyv0par 8i k3sih4l+ld 5 qv,z9c from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling fasteqpv5z4vi hk ,sa l03ric8 +9dlr when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet szl06d(a lm3 k4k vh;eis dropped from the same height. Ignore air resistance. Compals4k (a;m3v le6zh0kdre the times of fall of the two bullets.

  A plane flying horizontally at a speed of 104.6 a(2g cfu9y9 xlhm1mn9m/s and at an elevation of 194 m drops a package. 7.7 seconds later it drops a yg2fa9xmcmnu1h9l9 ( second package. How far apart will the two packages land on the ground?

  A package of supplies is droppe2n xb. aacp1 +nva4hi3d from a plane, and one second later a second package is dropped. Negleca.a ibxp3n2 1vh4cn+a ting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constantjfj 9 ne;qe*.3of h -vdyg0aq:d,s-qt speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of theh .oe-f v-d ;q*ajjt9:y0 ge3nf qds,q plane will

  The acceleration of gravity on the Moon is only one-sixth of that onr68k7.66qw h yhkh jbe Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth,6hy7 j ew.hkb 8q6rkh6 the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight)gqw pq+io26s , level road and pass a car traveling at 45 mi/h. The relative velocity of your c6p)q s2+ oiwgqar to the other car is

  You are trying to cross a river that flows due south with a str/tvw9;:qof a4qjj.t :njy(c a ong current. You start out in your motorboat on the east bank desiring to reach the west bank f:yjt toqc:qn(j9avaw/j 4. ;directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time ,s8i;i4inl yh;-:c hufyd ;7te1vws n will it take you to move 12 km downstream- uc nh ldi;iin s:te4;f17yyvs; h8,w, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an k/umv-jqt )y-r) et)sangle of 30 degrees below the +x axis. The y comsrmy))j-t tqv/ )- ukeponent of A is

  If a ball is thrown with a velocity of 25 m/s at an angle 709uyhpnihw /pmts+ 0of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a dirlhj5- uf3rtx 6wccje75+em 8h 4i7rpeection north of east and you end up 2.0 km north and several kilometers east. How many degrees j7p3ciumr-w8 x+reche h 75t 6flj4e5north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x compo5iyu5z9 b yfp.nent of its velocity is 8.00 m/s. The angle 9.ip5fb5y zu ybetween the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. Atsx .r x-v4/4oaarz4kf what angle is the Su44 aavkx o-f4z/rr .sxn elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-*uu0fssng b .b 8pg+6m1, 3), respectively. What are the componentfmnspb +6g 0u8sbu.*gs of the sum of these two vectors?

  Two vectors A and Bzxcw1f +6 a6vl have components (0, 1) and (-1, 3), respectively. What is magnitude of t+v6la wc zf1x6he sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + Byg f+l+iiy;5y . What is the magnitude of C ?+;igfyi +y 5ly

  A car travels 20 km West, then 20 xh vke80 7rs8:y yw6xekm South. What is the magnitude of its displacem:ys6x8w r7x8 hkeyev0ent?

  Three vectors, expressed in Cartesian coordinatep.)yefn )x ui2s, 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 coordinatuhu sf va(7 )y7t2j4jtk7v9nwev(m 5bes, 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 vechkvf .7uy-k cs 7hd j+7)zq)wttor B = (+3.0, -8.0), what is the magnitude of v+ ktqf.hk7hz vduy-7)cj7s )wector C = A - B ?

  A runner runs halfway around a circular path of radh4w a+v kl49koius 10 m. What is the displacemk 9klo+v4h 4waent of the jogger?

  Two forces are acting on o b9hf ./r eb;ch,mv8zf vg;*kan object as shown in Fig. below. What is the magnitude of thhe k,g.fvo; 8bv/f*hbzmr ; c9e resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the directiot jik*-t;1( nf/qykboi.uyx90laws3:n xd )m n of th.xbxy a nwk i*qo(tsfltk/i9y1 uj-; m0)3:nde resultant force?

  Vector A is 3.2 cm long and points along the positive x axis. Vector B is 5.d*dm:.-vsw , l1gt/tst m+mwyyznu7* q8o6kn4 cm y8 l+t v6sq w*td dn.u,toz 7 wys*:1mnm-/mgklong and points at $+44^{\circ}$ 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 70 cm long and p w1bgmc,: val1p+1uv eoints at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 27 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 horizontal 15zj i lwsq6djtsm r,,6hdb18ly with an initial speed of 26 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the totl s,bi 1wq86jjs md15 zhr,d6p of the cliff to the bottom to be 4.1 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a ve5eba ss0am:8a.5 v::uu*:a hr le yirnlocity of 5 m/s, from a bridge. It falls 14 m to the water beloa*5s.ua:0a8lbhv:irs yn um:era: 5ew. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from qj *x;-dykfs 5a point 21 m above the ground, strikes the ground after traveling horizontally a distance of 21xj fk-;d*syq 5 m. With what speed was it thrown?

  A jumper in the long-jump goes in0j h+ba+idl28 ;vb)ays0ra gz to the jump with a speed of 12 m/s at an angle 0zg;a2 8vihy++ sb)laj arb0dof $20^{\circ}$ 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 12 m/s at an anglfl-h,vk o7u.re of-r lovf, u.hk7 $40^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity oznafg/ ih; ogpjiv) *o7(0* / krlumy9f 31.1 m/s at an angle of $49.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initialjbt q-6p)/s/st ou(u 8vdonj7 velocity of 22.7 m/s at an angle of $15.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at ap;tynh7 ; z*i;fjg/10kk/iu (i ernxbn 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 horizontallydt2l d,r: qy 7fkemfq/fn, -(v at 18.4 $m/s$ from the roof of a building 32.1 $m$ 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 ground level with an initintss;zjy q+t; q: g5(m u*d mhxv*z4/pezc)5xal speed of 64.2 m/s at an anx5; jetv d4hzg:5 /cm y+zstu q(qpszx;)m*n*gle of $44.2^{\circ}$ 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),lksty1)fwg0 v(zzz/+ you can 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 2.0 m/s, the time it would tak zywft lgz10 +kz(s)v/e you to finish would be

  A plane has an air speed oflw6px 68 l *wu,prb1il 200 m/s due North, and is in a wind of 50.0 m/s to the West. T* p uxll8i16rwwblp,6 he plane's speed relative to the ground is

  A plane is flying due 0g o -16 ewzkf1on7qxzSouth ($270^{\circ}$) 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 c*b5byx,8oyv- xr *jnof 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 horizontally f rf ubw+ji;1-bires a projectile with speed 50.0 m/s i1ju i+;r-bwbf n 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 water is 8.0 m/s, is directed across a rivesl el7:m/ rs:vbc.ko)r with a current of 6.0 m/s. What is the speed of the boat as it crosses the rbr) ks./lvoems :l7c :iver?

  The driver of a motorboat that can move at 17 m/s in still wati)/(i1 -k )yaehe(lua a,sl pcer wishes to travel/l)h1cyea (( sapuli k-)a e,i directly across a river 0.7 km wide in which the current flows at 6.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move (b:cib (irj+*ty gq9aw (7bn hat 10 m/s in still water wishes to travel direbgq(w i+rc9*(bby7at :(hji nctly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite ban e3qd 6be8;ao/h0 - z-fqopqeyk in 6 min 40 s. Sheof/8 q 0e -63qpoaz -yqedeb;h is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly a++ hnr(7prr dycross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is t nyr7 hpd+(rr+he speed of the current?

  A boat, whose speed in still water is 1.02 m/s, must aim dktiq.ek 4m:7upstream at an angle of . k:74qedtmki$22.9^{\circ}$ (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)  $m/s$