Deck 3: Motion in Two Dimensions

Question 1

The sum of two vectors has the greatest magnitude when the angle between these two vectors is

Answer 1

Zero degrees

Question 2

The sum of two vectors has the smallest magnitude when the angle between these two vectors is

Answer 2

180 degrees

Question 3

Neglecting the effect of air friction, at what angle should a cannon be raised to achieve the greatest HEIGHT?

Answer 3

90.°

Question 4

Neglecting the effect of air friction, at what angle should a cannon be raised to achieve the greatest RANGE (horizontal distance)?

Question 5

If the magnitude of vector A is less than the magnitude of vector B, then the x component of A is less than the x component of B.

Question 6

If A+B= C and A+B=C, then the vectors A and B are oriented perpendicular relative to one other.

Question 7

If A-B=C and A-B=C, then the vectors A and B are oriented perpendicular relative to one other.

Question 8

If A+B=C and A² + B² = C2, then the vectors A and B are oriented perpendicular relative to one other.

Question 9

It is possible for the resultant of three vectors to equal zero.

Question 10

A car travels east with a constant velocity. The magnitude of the acceleration of the car is

A) zero.
B) decreasing.
C) increasing.
D) constant non-zero.
E) None of the other choices is correct.

Question 11

A car travels east and its velocity decreases. The acceleration of the car is in which of the following directions?

A) Westward
B) Northward
C) Eastward
D) Southward
E) Downward

Question 12

Under which of the following conditions would a car have a westward acceleration?

A) The car going eastward and its velocity is constant.
B) The car going eastward and its velocity is decreasing.
C) The car going eastward and its velocity is increasing.
D) The car going westward and its velocity is constant.
E) The car going westward and its velocity is decreasing.

Question 13

If the acceleration of an object is always directed perpendicular to its velocity, then

A) the object is t rest.
B) the object is slowing down.
C) the object is speeding up.
D) the object is turning.
E) this situation would not be physically possible.

Question 14

A vectorhas components A_x > 0, and A_y > 0, the angle that this vector makes with the positive x-axis must be in the range

A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.

Question 15

A vector has components A_x < 0, and A_y > 0, the angle that this vector makes with the positive x-axis must be in the range

A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.

Question 16

A vector has components A_x < 0, and A_y < 0, the angle that this vector makes with the positive x-axis must be in the range

A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.

Question 17

A vector A has components A_x > 0, and A_y < 0, the angle that this vector makes with the positive x-axis must be in the range

A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.

Question 18

A 200-lb force is pulling on an object, as shown in Figure 3-1.
Figure 3-1

The sign of the x and y components of the force are

A) x (negative), y (negative).
B) x (positive), y (positive).
C) x (negative), y (positive).
D) x (positive), y (negative).

Question 19

-Refer to Figure 3-2. The components of vectors A and B are

A) A_x = A sin90° B_x = B cos60° Ay = A cos90° By = B sin60°.
B) A_x = A cos90° B_x = B sin60° Ay = A sin90° By = B cos60°.
C) A_x = 0 B_x = B sin 30° Ay = 0 By = B cos30°.
D) A_x = A sin 90° B_x = B sin 30° Ay = 0 By = B cos30°.
E) A_x = A cos0° B_x = -B cos60° Ay = A cos90° By = B cos30°.

Question 20

Consider two vectors A and B in Figure 3-3:

The difference A-B is

A) choice (a).
B) choice (b).
C) choice (c).
D) choice (d).

Question 21

Consider two vectors A and B in Figure 3-4:
Figure 3-4

The difference B -A is

A) choice (a).
B) choice (b).
C) choice (c).
D) choice (d).

Question 22

Two displacement vectors have magnitudes of 5 m and 7 m, respectively. When these two vectors are added, the magnitude of the sum

A) is larger than 12 m.
B) could be as small as 2 m, or as large as 12 m.
C) is exactly 2 m.
D) is exactly 12 m.
E) is exactly 6 m.

Question 23

Three boys each pull with a 20-lb force on the same object, as shown in Figure 3-5.
Figure 3-5

The resultant force will be

A) 20 lb to the left.
B) zero.
C) 20 lb down.
D) 20 lb up.
E) cannot be determined; insufficient information

Question 24

Which of the following operations will not change a vector?

A) Multiply it by a constant factor.
B) Rotate it.
C) Subtract a constant vector from it.
D) Translate it parallel to itself.
E) Add a constant vector to it.

Question 25

Which of the following is a unit-vector?

A) _o a + t
B) (11eea3cc_49c3_d225_97f4_0fcc18817ac4_TB9720_11-11eea3cc_49c3_d225_97f4_0fcc18817ac4_TB9720_11_o) t
C) v cos $\theta$
D) sin² $\theta$ + cos² $\theta$
E) / x

Question 26

You toss a ball to your friend. When the ball reaches its maximum altitude, its velocity is

A) zero.
B) horizontal.
C) 9.8 m/s².
D) 9.8 m/s.
E) vertical.

Question 27

Consider a thrown ball which has reached its highest point in flight. The magnitude of the acceleration

A) reverses direction.
B) is 2*g.
C) is zero.
D) is less than it will be a short instant later.
E) is g.

Question 28

A stone is thrown horizontally from the top of a tower at the same instant that a ball is dropped vertically. Which object is traveling faster when it hits the level ground below?

A) It is impossible to tell from the information given.
B) the ball
C) the stone
D) Neither, since both are traveling at the same speed.

Question 29

You hit a tennis ball over the net. When the ball reaches its maximum height, its speed is

A) equal to its initial speed.
B) less than its initial speed.
C) g*t.
D) greater than its initial speed.
E) zero.

Question 30

An arrow is shot, from a bow, at an original speed of v_o. When it returns to the same horizontal level, its speed will be

A) 9.8 v_o.
B) 2 v_o.
C) 1/2 v_o.
D) v_o.
E) 4 v_o.

Question 31

You hit a handball too hard, and it lands horizontally on top of a roof. If its original velocity was v_o at an angle $\theta$ above the horizontal, then it lands on the roof with a velocity of

A) v_o sin $\theta$
B) zero
C) v_o cos $\theta$
D) 2 v_o
E) v_o

Question 32

You toss a ball to your friend. The ball reaches its maximum altitude

A) in half of the time it is in the air.
B) in less than half the time it is in the air.
C) in more than half the time it is in the air.

Question 33

A soccer ball is kicked with a velocity of 25 m/s at an angle of 45° above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory? (Neglect air friction.)

A) g upward
B) g sin(45°) upward
C) g downward
D) zero
E) g cos(45°) downward

Question 34

You toss a ball to a friend. When the ball reaches its maximum altitude, its acceleration

A) is 2*g.
B) changes sign.
C) is constant.
D) is g/2.
E) is zero.

Question 35

Bullet G is dropped, from rest, at the same time that another bullet H is fired horizontally from a rifle. If both bullets leave from the same height above the ground, then

A) not enough information is given to compare when they hit.
B) both bullets hit the ground at the same time.
C) bullet H hits the ground before bullet G does.
D) bullet G hits the ground before bullet H does.

Question 36

A pilot drops a bomb from a plane flying horizontally at a constant speed. When the bomb hits the ground, the horizontal location of the plane will

A) be behind the bomb.
B) be in front of the bomb.
C) be over the bomb.

Question 37

A package of supplies is dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packages will

A) be constant.
B) depend on their weight.
C) decrease.
D) be gt².
E) increase.

Question 38

A package of supplies is dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the relative velocity of the 1st package viewed from the second will

A) be constant.
B) increase.
C) decrease.
D) be zero.
E) depend upon their weight.

Question 39

If you increase the initial speed of a bullet by 10%, the resultant RANGE will increase by what percent (assume air resistance can be ignored)?

A) 11%
B) 5.0%
C) 20%
D) 21%
E) 10%

Question 40

When air resistance is a factor, maximum range is achieved when the projection angle is

A) less than 45.°
B) 90.°
C) 45.°
D) greater than 45.° but not 90.°

Question 41

Suppose that several projectiles are fired upward. Which one will be in the air longest? (R is range, h is highest elevation, and t is time of flight.)

A) The one with the highest maximum elevation, h
B) The one with the greatest initial velocity
C) The one with the minimum elevation, h
D) The one with the farthest range, R
E) The one for which the product of (R)(t)(h) is maximum

Question 42

You are serving the volleyball for the second time in a volleyball game. If the ball leaves your hand with twice the velocity it had on your first serve, its horizontal range R (compared to your first serve) would be

A) times as much.
B) twice as much.
C) 2 times as much.
D) four times as much.
E) half as much.

Question 43

At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range?

A) 30°
B) 0°
C) $\pi$ radians
D) 90°
E) 45°

Question 44

The acceleration of gravity on the 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 travel

A) one-sixth as far.
B) as far.
C) the same distance away.
D) 6 times as far.
E) 36 times as far.

Question 45

You throw a pebble upward as shown, with a velocity v_o at an angle ?, from a roof (at point J) Figure 3-6

If the pebble rises upward to h ft above the roof (to point K), then falls to the ground below (to point L), its speed when it hits the ground is

A) between vo and 2v_o
B) greater than 2 v_o
C) v_o
D) 2 v_o
E) v_o

Question 46

Consider throwing a shotput at a 45.° elevation. The ratio of range to height (R/h) would be

A) 2

B) 2²
C) 2⁴
D)

E) 2

Question 47

If you want to cross a river in a motorboat in the least amount of time (least time in water), you should head

A) the time will be independent of how you head your boat
B) slightly downstream.
C) directly downstream.
D) slightly upstream.
E) straight across the river.

Question 48

Consider a plane flying with groundspeed V_g and airspeed V_a in a wind with velocity V. Which of the following relationships is true?

A) V_g can be greater than V_a + V
B) V_g = V_a - V
C) V_g = V_a + V
D) V_g can be less than V_a + V
E) V_g can have any value between V_a + V and V_a - V

Question 49

Consider a velocity with components 36. m/s Westward and 22. m/s Northward. What is its magnitude and direction?

Question 50

A particle initially moving with a velocity 2 m/s experiences a constant acceleration of 1 m/s² in the +x-direction and -2 m/s² in the y-direction. What are the velocity components of the particle after 4 s?

Question 51

Two vectors A and B have components (0, 1, 2) and (-1, 3, 1), respectively.
(a) Determine the components of the sum of these two vectors.
(b) Determine the magnitude of the sum of these two vectors.

Question 52

-For the three vectors given in Figure 3-7, determine the vector "difference" - - https://d2lvgg3v3hfg70.cloudfront.net/TB9720/.

Question 53

-Given the three vectors in Figure 3-7, determine the vector sum + + https://d2lvgg3v3hfg70.cloudfront.net/TB9720/.

Question 54

-For the three vectors shown in Figure 3-7, determine +- https://d2lvgg3v3hfg70.cloudfront.net/TB9720/.

Question 55

The magnitude of a vector is 3.1 units and its x component is 0 units. What are the possible y components and respective angles with the x-axis of the vector?

Question 56

Lisa throws a stone horizontally from the roof edge of a 50. meter high dormitory. It hits the ground at a point 60. m from the building. Find the time of flight.

Question 57

A marble rolls off the edge of a table top with a speed of 2.0 m/s. What is the magnitude of its velocity 0.10 s later?

Question 58

A mortar shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below. How far from the base of the cliff does the mortar shell strike the ground?

Question 59

A rifle bullet is fired at an angle of 30° 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?

Question 60

Suppose David Ortiz hits a home run which travels 361. feet (110. m). Assuming it left the bat at 50.°, how fast was it hit?

Question 61

Suppose Sammy Sosa hits a home run which travels 361. ft (110. m). Leaving the bat at 50 degrees above the horizontal, how high did it travel?

Question 62

A marble moving 1.48 m/s rolls off the top edge of a 125. cm high table.
(a) How far from the base of the table did it strike the floor?
(b) How long was it "in flight"?

Question 63

A hunter points a rifle horizontally 3.30 m above the ground. The bullet leaves the barrel at 325. m/s.
(a) How long did it take for the bullet to strike the ground?
(b) How far horizontally did it travel?

Question 64

A girl throws a rock horizontally with a speed of 12.0 m/s from a bridge. It falls 2.28 s before reaching the water below.
(a) How high is the bridge from the water below?
(b) How far horizontally does the rock travel before striking the water?

Question 65

Misty throws a stone horizontally from the roof edge of a 50. meter high dormitory. It hits the ground at a point 60. m from the building.
(a) Determine the horizontal component of velocity just before hitting the ground.
(b) What vertical speed did it have just before hitting the ground?

Question 66

Daisy throws a rock horizontally with a speed of 12.0 m/s from a bridge. It falls 2.28 s before reaching the water below.
(a) When the rock hits the water it is traveling with what horizontal component of velocity?
(b) What was the total speed just before hitting the water?

Question 67

How high does a bullet travel after leaving the barrel of a rifle at 225. m/s with
an angle of 66.° above the horizontal? Also what is its range (ignore air friction)?

Question 68

A bullet left the muzzle of a gun at 150. m/s and attains a height of 0.57 km. Initially the velocity was angled how many degrees above the horizontal?

Question 69

In attempting to jump up a waterfall, a salmon leaves the water 2.0 m from the base of the waterfall. With what minimum speed must it leave the water in order just to make it up a waterfall 1.6 m high?

Question 70

A child drops a toy at rest from a point 4.0 m above the ground at the same instant her friend throws a ball upward at 6 m/s from a point 1.0 m above the ground. At what distance above the ground do the ball and the toy cross paths?

Question 71

A car and a truck are traveling in the same direction along a straight section of highway. The car is moving at 55. mph and the truck is moving 45. mph. What is the velocity of the truck relative to the car?

Question 72

A car and a truck are traveling in the same direction along a straight section of highway. The car is moving at 55. mph and the truck is moving 45. mph. What is the velocity of the car relative to the truck?

Question 73

An airplane with an airspeed of 120. km/h is headed 30.0° East of North in a wind blowing due West at 30. km/h. What is the groundspeed of the plane?

Question 74

Billy swims to a point straight across a 100. m wide river that flows at 1.2 m/s. How long does it take him to swim to the other side?

Question 75

Holly intends to swim to a point straight across a 100. m wide river that flows at 1.2 m/s. If she can swim 2.5 m/s in still water, at what angle must she swim upstream to achieve her goal?

Question 76

A pickup truck moves 25. m/s Eastward. Jerry is standing in the back and throws a baseball in what to him is the Southwest direction at 28. m/s (with respect to the truck). A person at rest would see the ball moving HOW FAST in WHAT DIRECTION?

Question 77

An airplane is pointed in the NE direction and is moving 71. m/s with respect to the air. The jetstream (moving air) carries the plane 30. m/s toward the East. What is the velocity of the plane relative to the ground?

Question 78

The driver of a motorboat that can move at 10 m/s wishes to travel directly across a narrow strait in which the current flows at 5 m/s.
(a) At what angle upstream should the driver head the boat?
(b) How long will it take to cross a distance of 1.6 km?

Question 79

A boat has a velocity 12. km/hr Southward and 16. km/hr Westward. What is its speed and how long does it take to travel 94. km?

Question 80

A 960. m wide river flows at 16. m/s as shown in Figure 3-8. Alice and John have a race in identical boats which travel 20. m/s in still water. Alice leaves point A and steers so that she goes straight to point B directly across and then back to A. John steers up to point C (960. m upstream) and then returns to A. Figure 3-8

(a) Which person arrived back at A first?
(b) How much sooner did the winner arrive back at A?