Essential University Physics, 3e (Wolfson) Chapter 3 Motion in Two Two and Three Dimensions
3 . 1 Conc e p t ua lQue s t i o ns 1) Shown below are the velocity and acceleration vectors for a person p erson in several different types of motion. In which case is the person slowing down and turning to his right? A)
B)
C)
)
!)
Answer" B #ar" 1
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%) *hile an ob+ect is in pro+ectile motion ,with upward being p ositive) with no air resistance A) the hori-ontal component of its velocity remains constant and the hori-ontal component of its acceleration is eual to / g g . B) the hori-ontal component of its velocity remains constant and the vertical component of its acceleration is eual to / g g . C) the hori-ontal component of its velocity remains constant and the vertical component of its acceleration is eual to -ero. ) the vertical component of both its velocity and its acceleration remain constant. !) the vertical component of its velocity remains constant and the vertical component of its acceleration is eual to / g g . Answer" B #ar" 1
0) or general pro+ectile motion when the pro+ectile is at the highest point of its tra+ectory A) its acceleration is -ero. B) its velocity is perpendicular to the acceleration. C) its velocity and acceleration are both -ero. ) the hori-ontal component of its velocity is -ero. !) the hori-ontal and vertical components of its velocity are -ero. Answer" B #ar" 1
2) Alice and 3om 3om dive from an overhang into the la4e below. 3om 3om simply drops straight down from the edge but Alice ta4es a running start and +umps with an initial hori-ontal velocity of %5 m6s. 7either person e8periences any significant air resistance. 9ust as they reach the la4e below A) the speed of Alice is larger than that of 3om. B) the splashdown speed of Alice Alice is larger than that of 3om. C) they will both have the same speed. ) the speed of 3om 3om will always be :.; m6s larger than that of Alice. !) the speed of Alice will always be %5 m6s larger than that of 3om. Answer" A #ar" 1
5) Alice and 3om 3om dive from an overhang into the la4e below. 3om 3om simply drops straight down from the edge but Alice ta4es a running start and +umps with an initial hori-ontal velocity of %5 m6s. 7either person e8periences any significant air resistance. Compare the time it ta4es each of them to reach the la4e below. A) Alice reaches the surface of the la4e first. B) 3om 3om reaches the surface of the la4e first. C) Alice and 3om 3om will reach the surface of the la4e at the same time. Answer" C #ar" 1
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') 9an and s roc4. If air resistance is negligible which roc4 hits the ground first? A) 3hey hit at the same time. B) 9an>s roc4 hits first. C) s roc4 hits first. ) It is impossible to 4now from the information given. Answer" A #ar" 1
) A mon4ey is sitting at the top of a tree %& m above ground level. A person standing on the ground wants to feed the mon4ey. @e uses a bow and arrow to launch the food to the mon4ey. If the person 4nows that the mon4ey is going to drop from the tree at the same instant that the person launches the food how should the person aim the arrow containing the food? Air resistance is small enough to be ignored. A) @e should aim it at the mon4ey. B) @e should aim it below the mon4ey. C) @e should aim it above the mon4ey. Answer" A #ar" 1
;) A pilot drops a pac4age from a plane flying hori-ontally at a constant speed. 7eglecting air resistance when the pac4age hits the ground the hori-ontal location of the plane will A) be behind the pac4age. B) be over the pac4age. C) be in front of the pac4age. ) depend of the speed of the plane when the pac4age was released. Answer" B #ar" 1
:) or an ob+ect in uniform circular motion its velocity and acceleration vectors are always perpendicular to each other at every point in the path. A) 3rue B) alse Answer" A #ar" 1
1&) If an ob+ect travels at a constant speed in a circular path the acceleration of the ob+ect is A) larger in magnitude the smaller the radius of the circle. B) in the same direction as the velocity of the ob+ect. C) smaller in magnitude the smaller the radius of the circle. ) in the opposite direction of the velocity of the ob+ect. !) -ero. Answer" A #ar" 1
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11) (oint P in the figure indicates the position of an ob+ect traveling at constant speed cloc4wise around the circle. *hich arrow best represents the direction of the acceleration of the ob+ect at point P ?
A)
B)
C) )
!)
Answer" #ar" 1
1%) If you set the cruise control of your car to a certain speed and ta4e a turn the speed of the car will remain the same. Is the car accelerating? A) es B) 7o Answer" A #ar" 1
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10) *hich of the following is an accurate statement? A) 3he magnitude of a vector can be -ero even though one of its components is not -ero. B) It is possible to add a scalar uantity to a vector. C) !ven though two vectors have uneual magnitudes it is possible that their vector sum is -ero. ) otating a vector about an a8is passing through the tip of the vector does not change the vector. !) 3he magnitude of a vector is independent of the coordinate system used. Answer" ! #ar" 1
12) If
-
& then the vectors
and
have eual magnitudes and are directed in the
opposite directions from each other. A) 3rue B) alse Answer" B #ar" 1
15) Dnder what condition is E
-
| A + B?
A) 3he magnitude of vector
is -ero.
B) #ectors
and
are in opposite directions.
C) #ectors
and
are in the same direction.
) #ectors
and
are in perpendicular directions.
!) 3he statement is never true. Answer" B #ar" 1
1') If A > B under what condition is E
-
| = A - B?
A) 3he statement is never true. B) #ectors
and
are in opposite directions.
C) #ectors
and
are in the same direction.
) #ectors
and
re in perpendicular directions.
!) 3he statement is always true. Answer" C #ar" 1
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1) or the vectors shown in the figure e8press vector
Answer"
in terms of vectors
and
.
/
#ar" 1
1;) 3he magnitude of a vector can never be less than the magnitude of one of its components. A) 3rue B) alse Answer" A #ar" 1
1:) If the magnitude of vector of
is less than the magnitude of vector
is less than the x component of
then the x component
.
A) 3rue B) alse Answer" B #ar" 1
%&) If the eastward component of vector
is eual to the westward component of vector
and
their northward components are eual. *hich one of the following statements about these two vectors is correct? A) #ector B) #ectors C) #ector
is parallel to vector and
.
point in opposite directions.
is perpendicular to vector
.
) 3he magnitude of vector
is eual to the magnitude of vector
!) 3he magnitude of vector
is twice the magnitude of vector
.
.
Answer" #ar" 1
%1) If all the components of a vector are eual to 1 then that vector is a unit vector. A) 3rue B) alse Answer" B #ar" 1
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3 . 2 Pr o bl e ms 1) Fb+ect A has a position as a function of time given by A,t ) ,0.&& m6s)t G ,1.&& m6s%)t % . Fb+ect B has a position as a function of time given by B,t ) ,2.&& m6s)t G ,/1.&& m6s%)t % . All uantities are SI units. *hat is the distance between ob+ect A and ob+ect B at time A) 02.' m B) 15.& m C) 1;.0 m ) 0.2' m !) %:.; m Answer" C #ar" 5
%) An ob+ect has a position given by
H%.& m G ,5.&& m6s)t G H0.& m / ,%.&& m6s%)t % where
uantities are in SI units. *hat is the speed of the ob+ect at time A) '.2& m6s B) :.20 m6s C) .&& m6s ) .'5 m6s !) 10.& m6s Answer" B #ar" 5
0) An ob+ect has a position given by
H%.& m G ,0.&& m6s)t G H0.& m / ,%.&& m6s%)t % where
all uantities are in SI units. *hat is the magnitude of the acceleration of the ob+ect at time t %.&& s? A) 1.&& m6s% B) &.&& m6s% C) &.5%% m6s% ) 2.&& m6s% !) %.&& m6s% Answer" #ar" 5
2) 3he hori-ontal coordinates of a
in a strong wind are given by
where x and y are in meters and t is in seconds. ,a) *hat is the acceleration of the risbee? Jive a magnitude and a direction measuring angles from the positive x direction. ,b) *hat is the magnitude of the velocity at accurate to the nearest Answer" ,a) 1& m6 0%0= ,b) 2 m6s #ar" 1
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5) An electron moves with a constant hori-ontal velocity of and no initial vertical velocity as it enters a deflector inside a 3# tube. 3he electron stri4es the screen after traveling hori-ontally and vertically upward with no hori-ontal acceleration. *hat is the constant vertical acceleration provided by the deflector? ,3he effects of gravity can be ignored.) A) %.5 × 1&12 m6s% B) ;.0 × 1&% m6s% C) 1.2 × 1&2 m6s% ) 1.% × 1&12 m6s% Answer" A #ar" 5&G
') A hoc4ey puc4 slides off the edge of a table at point A with an initial velocity of %&.& m6s and e8periences no air resistance. 3he height of the tabletop above the ground is %.&& m. ,a) *hat is the speed ,not the velocity) of the pu c4 +ust before it touches the ground? ,b) *hat is the distance between point A and the point where the puc4 hits the ground? Answer" ,a) %1.& m6s ,b) 1%.: m #ar" 1
) A hoc4ey puc4 slides off the edge of a table with an initial velocity of %;.& m6s. and e8periences no air resistance. 3he height of the tabletop above the ground is %.&& m. *hat is the angle below the hori-ontal of the velocity of the puc4 +ust before it hits the ground? A) .%= B) %.'= C) 1%.;= ) 1%.'= !) 01.;= Answer" #ar" '
;) A boy throws a roc4 with an initial velocity of at 0&.&= above the hori-ontal. If air resistance is negligible how long does it ta4e for the roc4 to reach the ma8imum height of its tra+ectory? A) &.11& s B) &.1:2 s C) &.%15 s ) &.0&0 s Answer" A #ar" 5&G
:) *hat is the ma8imum distance we can shoot a dart from ground level provided our toy dart gun gives a ma8imum initial velocity of and air resistance is negligible? A) &.;: m B) 1.5; m C) 1.0: m ) &.0:2 m Answer" A #ar" 5&G ; Copyright $ %&1' (earson !ducation Inc.
1&) A catapult is tested by oman legionnaires. 3hey tabulate the results in a papyrus and %&&& years later the archaeological team reads ,distances translated into modern units)" angle of landing height launch height. *hat is the initial velocity of launch of the boulders if air resistance is negligible? A) 22 m6s B) 1.2 m6s C) %% m6s ) &.': m6s Answer" A #ar" %&
11) A hobby roc4et reaches a height of resistance. *hat was the angle of launch? A) ':.&= B) '.2= C) %%.'= ) 22.;= Answer" A
and lands
from the launch point with no air
#ar" 5&G
1%) A ball is thrown at a '&.&= angle above the hori-ontal across level ground. It is thrown from a height of %.&& m above the ground with a speed of %&.& m6s and e8periences no appreciable air resistance. 3he time the ball remains in the air before stri4ing the ground is closest to A) 1'.% s. B) 0.& s. C) 0.0% s. ) 0.50 s. !) 0.'2 s. Answer" ! #ar" 5
10) A roc4 is thrown at a window that is located 1;.& m above the ground. 3he roc4 is thrown at an angle of 2&.&= above hori-ontal. 3he roc4 is thrown from a height of %.&& m above the ground with a speed of 0&.& m6s and e8periences no appreciable air resistance. If the roc4 stri4es the window on its upward tra+ectory from what hori-ontal distance from the window was it released? A) 50.% m B) 2;. m C) 1.' m ) %:.; m !) %.0 m Answer" ! #ar" 1
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12) An airplane is flying at a speed of %.&& 1&% m6s in level flight at an altitude of ;.&& 1&% m. A pac4age is to be dropped from the airplane to land on a target on the ground. Ignore air resistance. ,a) At what hori-ontal distance away from the target should the pac4age be released so that it lands on the target? ,b) In what direction relative to the hori-ontal will the pac4age be traveling when it hits the ground? Answer" ,a) %.5' 4m ,b) 0%.1= below the hori-ontal #ar" 1
15) A child throws a ball with an initial speed of ;.&& m6s at an angle of 2&.&= above the hori-ontal. 3he ball leaves her hand 1.&& m above the ground and e8perience negligible air resistance. ,a) @ow far from where the child is standing does the ball hit the ground? ,b) @ow long is the ball in flight before it hits the ground? Answer" ,a) .2' m ,b) 1.%% s #ar" 1
1') A child throws a ball with an initial speed of ;.&& m6s at an angle of 2&.&= above the hori-ontal. 3he ball leaves her hand 1.&& m above the ground and e8perience negligible air resistance. ,a) *hat is the magnitude of the ball>s velocity +ust before it hits the ground? ,b) At what angle below the hori-ontal does the ball approach the ground? Answer" ,a) :.12 m6s ,b) 2.:= #ar" 1
1) A pro+ectile is fired from point 0 at the edge of a cliff with initial velocity components of and
as shown in the figure.3he pro+ectile rises and then falls into the
sea at point P . 3he time of flight of the pro+ectile is 2&.& s and it e8periences no appreciable air resistance in flight. *hat is the magnitude of the velocity of the pro+ectile %1.& s after it is fired?
Answer" '.2 m6s #ar" 1
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1;) A pro+ectile is fired from point 0 at the edge of a cliff with initial velocity components of v& x '&.& m6s and v& y 15 m6s as shown in the figure. 3he pro+ectile rises and then falls into the sea at point P . 3he time of flight of the pro+ectile is 2&.& s and it e8periences no appreciable air resistance in flight. *hat is the height of the cliff?
Answer" ;2& m #ar" 1
1:) A hi4er throws a stone from the upper edge of a vertical cliff. 3he stone>s initial velocity is %5.& m6s directed at 2&.&= with the face of the cliff as shown in the figure. 3he stone hits the ground 0.5 s after being thrown and feels no appreciable air resistance as it falls. ,a) *hat is the height of the cliff? ,b) @ow far from the foot of the cliff does the stone land? ,c) @ow fast is the stone moving +ust before it hits the ground?
Answer" ,a) 121 m
,b) '&.0 m
,c) 5;.% m6s
#ar" 1
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%&) A pro+ectile returns to its original height 2.&; s after being launched during which time it travels '.% m hori-ontally. If air resistance can be neglected what was the pro+ectile>s initial speed? Answer" %.2 m6s #ar" 1
%1) A plane flying at &.& m6s suddenly stalls. If the acceleration during the stall is :.; m6s% directly downward the stall lasts 5.& s and the plane was originally climbing at %5= to the hori-ontal what is the velocity after the stall? A) '' m6s at 1= below the hori-ontal B) '' m6s at 1= above the hori-ontal C) ;& m6s at 0= below the hori-ontal ) ;& m6s at 0= above the hori-ontal Answer" A #ar" 1
%%) A rescue plane flying hori-ontally at spots a survivor in the ocean directly below and releases an emergency 4it with a parachute. . Because of the shape of the parachute it e8periences insignificant hori-ontal air resistance. If the 4it descends with a constant vertical acceleration of how far away from the survivor will it hit the waves? A) 52 m B) 2.52 4m C) 2&' m ) '&% m Answer" A #ar" 5&G
%0) An airplane flies between two points on the ground that are 5&& 4m apart. 3he destination is directly north of the origination of the flight. 3he plane flies with an air speed of 1%& m6s. If a constant wind blows at 1&.& m6s due west during the flight what direction must the plane fly relative to north to arrive at the destination? A) 2.;= east of north B) 2.'= east of north C) ;5.%= west of north ) 2.;= west of north !) 2.'= west of north Answer" A #ar" 1
%2) A plane has an eastward heading at a speed of 15' m6s ,relative to the air). A %&.& m6s wind is blowing southward while the plane is flying. 3he velocity of the plane relative to the ground is A) 15 m6s at an angle .01= south of east. B) 15 m6s at an angle .01= east of south. C) 155 m6s at an angle .0'= south of east. ) 155 m6s at an angle .0'= east of south. !) 15 m6s at an angle .0'= south of east. Answer" A #ar" 1 1% Copyright $ %&1' (earson !ducation Inc.
%5) A swimmer heading directly across a river %&& m wide reaches the opposite ban4 in during which time she is swept downstream 2;& m. ,a) @ow fast can she swim in still water? ,b) *hat is the speed of the current? Answer" ,a) &.5& m6s ,b) 1.% m6s #ar" 1
%') A small boat is moving at a velocity of
when it is accelerated by a river current
perpendicular to the initial direction of motion. If the acceleration of the current is &.5& m6s% what will be the new velocity of the boat after A) %5.0 m6s at ;%.2= from initial direction of motion B) %5.0 m6s at .5:= from initial direction of motion C) '2&.1 m6s at ;%.2= from initial direction of motion ) '2&.1 m6s at .5:= from initial direction of motion Answer" A #ar" 5&G
%) ou want to swim straight across a river that is wide. ou find that you can do this if you swim at an angle of θ %;= from the upstream direction at a constant rate of relative to the water. At what rate does the river flow? 3he angle θ is measured from the river ban4 ,directly upstream is while directly across the river is A) 1.0 m6s B) &.& m6s C) 1.' m6s ) 1.; m6s Answer" A #ar" 12
%;) A long/distance swimmer is able to swim through still water at 2.& 4m6h. She wishes to try to swim from (ort Angeles *ashington directly north to #ictoria British Columbia a distance of 5& 4m. An ocean current flows through the Strait of 9uan de uca from west to east at 0.& 4m6h. In what direction ,relative to north) should she swim to ma4e the crossing along a straight line between the two cities? A) 0= west of north B) 0= east of north C) 21= west of north ) 21= east of north !) 2:= west of north Answer" ! #ar" 1
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%:) A plane flies directly between two cities A and B which are separated by %0&& mi. rom A to B the plane flies into a '5 mi6h headwind. Fn the return trip from B to A the wind velocity is unchanged. 3he trip from B to A ta4es less than the trip from A to B. *hat is the airspeed of the plane assuming it is the same in both directions? A) 50& mi6h B) 2&& mi6h C) 2;& mi6h ) '1& mi6h Answer" A #ar" 01
0&) A cart is moving with a constant hori-ontal velocity of 5.&& m6s. A small pebble is launched from the front of the cart with a velocity of ;.&& m6s at '&.&= above the hori-ontal as measured relative to the cart ,see figure) and e8periences no significant air resistance. 9ust as the pebble returns to the level from which it was launched its distance from the front of the cart is closest to
A) %.;0 m. B) 2.'& m. C) 5.'' m. ) :.1: m. !) 11.0 m. Answer" C #ar" 1
01) A ball is tied to the end of a cable of negligible mass. 3he ball is spun in a circle with a radius %.&& m ma4ing .&& revolutions every 1&.& seconds. *hat is the magnitude of the acceleration of the ball? A) '.: m6s% B) 0;. m6s% C) %:.0 m6s% ) 12.; m6s% !) 2.% m6s% Answer" B #ar" 1
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0%) An electrical motor spins at a constant If the armature radius is what is the acceleration of the outer edge of the armature? A) %2&0 m6s% B) ;22.2 m6s% C) %211&& m6s% ) ;2.2& m6s% Answer" A #ar" 5&G
00) A satellite orbits the earth a distance of 1.5& K 1& m above the planet>s surface and ta4es ;.'5 hours for each revolution about the earth. 3he earth>s radius is '.0; K 1&' m. 3he acceleration of this satellite is closest to A) &.&':& m6s%. B) &.;& m6s%. C) 1.:1 m6s%. ) %.% m6s%. !) :.;& m6s%. Answer" B #ar" 1
02) An aircraft performs a maneuver called an Laileron roll.L uring this maneuver the plane turns li4e a screw as it maintains a straight flight path which sets the wings in circular motion. If it ta4es it 05 s to complete the circle and the wingspan of the plane is 11 m what is the acceleration of the wing tip? A) &.1; m6s% B) &.:: m6s% C) 5.' m6s% ) 1.& m6s% Answer" A #ar" 5&G
05) An ob+ect moves in a circle of radius R at constant speed with a period T . If you want to change only the period in order to cut the ob+ect>s acceleration in half the new period should be A) T 62. B) T 6%. C) T 6 . ) T . !) 2T . Answer" #ar" 1
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0') A wind farm generator uses a two/bladed propeller ,see figure) mounted on a pylon at a height of %& m. 3he length of each propeller blade is 1% m. A small piece from the tip of the propeller brea4s off when the propeller is vertical. At that instant the period of the motion of the propeller is 1.% s. 3he fragment flies off hori-ontally falls with negligible air resistance and stri4es the ground at P . ,a) @ow far is point P from the base of the pylon? ,b) At what angle with respect to the vertical is the fragment moving +ust as it stri4es the ground at P ?
Answer" ,a) 1'& m
,b) ';=
#ar" 1
0) A dis4/shaped space station 15 m in diameter spins uniformly about an a8is perpendicular to the plane of the dis4 through its center. @ow many rpm ,rev6min) must this dis4 ma4e so that the acceleration of all points on its rim is g6%? Answer" %.%' rev6min #ar" 1
0;) 3wo particles A and B are in uniform circular motion about a common center. 3he acceleration of particle A is ;.5 times that of particle B. 3he period of particle B is %.& times the period of particle A. 3he ratio of the radius of the motion of particle A to that of particle B is closest to A) r A6r B %.1. B) r A6r B 2.0. C) r A6r B 1;. ) r A6r B &.%2. !) r A6r B 1. Answer" A #ar" 5&G
0:) ou wal4 to the north then turn '&= to your right and wal4 another you from where you originally started? A) ; m B) 5& m C) :2 m ) 2' m Answer" A #ar" 01
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@ow far are
2&) #ectors of vector vector
and
are shown in the figure. #ector
is 1'.& units and the magnitude of vector
is given by
/
. 3he magnitude
is .&& units. *hat is the magnitude of
?
A) :.&& B) :.50 C) 15.5 ) 1'.% !) 1.5 Answer" #ar" 1
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21) #ectors of vector vector
and
are shown in the figure. #ector
is 1'.& units and the magnitude of vector
is given by
/
. 3he magnitude
is .&& units. *hat is the angle of
measured countercloc4wise from the G x/a8is?
A) 1'.:= B) %%.2= C) 0.1= ) %;= !) %:%= Answer" #ar" 1
2%) A rabbit trying to escape a fo8 runs north for ;.& m darts northwest for 1.& m then drops 1.& m down a hole into its burrow. *hat is the magnitude of the net displacement of the rabbit? A) ;.; m B) ;.1 m C) '' m ) 1& m Answer" A #ar" 5&G
20) ou wal4 50 m to the north then turn '&= to your right and wal4 another etermine the direction of your displacement vector. !8press your answer as an angle relative to east. A) '0= 7 of ! B) 5&= 7 of ! C) 5= 7 of ! ) ':= 7 of ! Answer" A #ar" 5&G
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22) #ector
has a magnitude 5.&& and points in a direction 2&.&= cloc4wise from the negative y
a8is. *hat are the x and y components of vector
.
A) A8 0.;0 and Ay 0.%1 B) A8 0.;0 and Ay /0.%1 C) A8 /0.%1 and Ay /0.;0 ) A8 /0.%1 and Ay 0.;0 !) A8 2.%: and Ay %.1' Answer" C #ar" 5
25) 3he components of vector
are
G 0.:& and
countercloc4wise from the G8/a8is to vector
/2.&&. *hat is the angle measured
?
A) 012= B) 102= C) %%2= ) 10'= !) 2'.&= Answer" A #ar" 1
2') #ector
has a magnitude of 5.5 cm and points along the x/a8is. #ector
of .5 cm and points at G0&= above the negative x/a8is. ,a) etermine the x and y components of #ector
.
,b) etermine the x and y components of #ector ,c) etermine x and y components of the sum of these two vectors. ,d) etermine the magnitude and direction of the sum of these two vectors. Answer" ,a) 5.5 cm & ,b)
/'.5 cm
0.; cm
,c) /1.& cm 0.; cm ,d) 0.: cm at 5= above / x/a8is #ar" 1
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has a magnitude
2) #ector
has a magnitude of 5.& cm and points at 0&= above the positive x/a8is. #ector
has a magnitude of %5.& cm and points along the negative x/a8is. #ector
has a magnitude of
2&.& cm and points at 25= below the negative x/a8is. ,a) etermine the x and y components of #ector
.
,b) etermine the x and y components of #ector
.
,c) etermine the x and y components of #ector
.
,d) etermine x and y components of the sum of these three vectors. ,e) etermine the magnitude and direction of the sum of these three vectors. Answer" ,a) '5 cm 0; cm ,b)
/%5 cm
&
,c)
/%; cm
/%; cm
,d) 1% cm :.% cm ,e) 15 cm at 0;= above G x/a8is #ar" 1
2;) A helicopter is flying hori-ontally with a speed of 222 m6s over a hill that slopes upward with a %M grade ,that is the LriseL is %M of the LrunL). *hat is the component of the helicopter>s velocity perpendicular to the sloping surface of the hill? A) ;.: m6s B) %%& m6s C) 205 m6s ) 222 m6s Answer" A #ar" 5&G
2:) An apple falls from an apple tree growing on a % &= slope. 3he apple hits the ground with an impact velocity of 1'.% m6s straight downward. *hat is the component of the apple>s impact velocity parallel to the surface of the slope? A) 5.5 m6s B) ;. m6s C) 1% m6s ) 15 m6s Answer" A #ar" 5&G
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5&) 3he components of vector are given are
/'.1 and
are
G%.% and
/'.: and the components of vector
/%.%. *hat is the magnitude of the vector
/
?
A) :.5 B) '.1 C) :.: ) :1 !) &.' Answer" A #ar" 5&G
51) 3he components of vector are
/' and
are
/0.5 and
/:. and the components of vector
G;.1. *hat is the angle ,less than 1;& degrees) between vectors
and
A) 1%2= B) 5'= C) 1= ) 1'0= !) 1&'= Answer" A #ar" 5&G
5%) An airplane undergoes the following displacements" irst it flies '' 4m in a direction 0&= east of north. 7e8t it flies 2: 4m due south. inally it flies 1&& 4m 0&= north of west. Dsing vector components determine how far the airplane ends up from its starting point. A) : 4m B) ;1 4m C) ;% 4m ) ; 4m !) ' 4m Answer" A #ar" 1
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50) In the figure the magnitude of vector units. *hat vector
is 1;.& units and the magnitude of vector
must be added to the vectors
and
is 1%.&
so that the resultant of these three
vectors points in the / x direction and has a magnitude of .5& units? Dse vector components to find your answer and e8press vector
by giving its magnitude and the angle it ma4es with the
G x/a8is ta4ing countercloc4wise to be positive.
Answer" 15.5 %&:= #ar" 1
52) 3hree forces are e8erted on an ob+ect placed on a tilted floor. orces are vectors. 3he three forces are directed as shown in the figure. If the forces have magnitudes = 1.& 7 = ;.& 7 and net
= .& 7 where 7 is the standard unit of force what is the component of the net force 1G
%G
0 parallel to the floor?
A) %.5 7 B) 5.1 7 C) '.& 7 ) .; 7 Answer" A #ar" %: %% Copyright $ %&1' (earson !ducation Inc.
55) As shown in the figure three force vectors act on an ob+ect. 3he magnitudes of the forces as shown in the figure are ;&.& 7 '&.& 7 and 2&.& 7 where 7 is the standard SI unit of force. 3he resultant force acting on the ob+ect is given by
A) 1;& 7 at an angle '&.&= with respect to G x/a8is. B) '&.& 7 at an angle :&.&= with respect to G x/a8is. C) %&.& 7 at an angle 02.0= with respect to G x/a8is. ) 05.5 7 at an angle 02.0= with respect to G x/a8is. !) 2&.& 7 at an angle '&.&= with respect to +x/a8is. Answer" #ar" 1
5') A teacher sends her students on a treasure hunt. She gives the following instructions" 1. *al4 0&& m north %. *al4 2&& m northwest 0. *al4 && m east/southeast and the treasure is buried there. As all the other students wal4 off following the instructions 9ane physics student uic4ly adds the displacements and wal4s in a straight line to find the treasure. @ow far and in what direction does 9ane need to wal4? A) 1; m in a direction '.0= north of east B) 2;1 m in a direction 2&.:= north of east C) 0:: m in a direction 5%.5= north of east ) %;2 m in a direction %;.%= west of north !) 3he treasure position cannot be reached in one straight wal4. Answer" B #ar" 1
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5) #ector
/0.&& G 0.&& and vector
0.&& G 2.&& . *hat is vector
G
?
A) &.&& G 0.&& B) .&& G .&& C) /0.&& G .&& ) &.&& G .&& !) /0.&& /0.&& Answer" #ar" 1
5;) #ector
1.&& G /%.&& and vector
direction of vector
G
0.&& G 2.&& . *hat are the magnitude and
?
A) .%1 in a direction 00.= countercloc4wise from the positive x a8is B) '.&& in a direction '0.2= countercloc4wise from the positive x a8is C) 2.2 in a direction '.02= countercloc4wise from the positive x a8is ) 2.2 in a direction %'.'= countercloc4wise from the positive x a8is !) .%1 in a direction 5'.0= countercloc4wise from the positive x a8is Answer" #ar" 1
5:) *hat is the magnitude of / 2.&&
and
+
+
where
1.&& G 2.&& / 1.&& ,
0.&& / 1.&&
/1.&& G 1.&& ?
A) .& B) %.&& C) 1&.' ) '.; !) ;.1% Answer" A #ar" :
'&) If
G2 / % / 0
magnitude of
/
and
/2 /% / 0
which of the following numbers is closest to the
?
A) ; B) C) : ) 1& !) 11 Answer" A #ar" 5&G
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'1) #ector
/1.&& G /%.&& and vector
direction of vector
0.&&
0.&& G 2.&& . *hat are the magnitude and
G %.&& ?
A) 0.'1 in a direction /5'.0= countercloc4wise from the positive x/a8is B) 0.'1 in a direction 5'.0= countercloc4wise from the positive x/a8is C) 0.'1 in a direction 00.= countercloc4wise from the positive x/a8is ) 5.&& in a direction 5'.0= countercloc4wise from the positive x a8is !) '.% in a direction 02.2= countercloc4wise from the positive x/a8is Answer" C #ar" 1
'%) #ectors
and
are shown in the figure. *hat is
A) 01.; B) /0%.& / %.&& C) 1&%; ) 02.& !) /%.&& / 0%.& Answer" A #ar" 1
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