Question 1

Arvin the Ant is on a picnic table.He travels 35 cm eastward,then 20 cm northward,and finally 5 cm westward.What is the magnitude of Arvin's net displacement?
​
A) 60 cm
B) 45 cm
C) 40 cm
D) 36 cm
E) ​21 cm

Accepted Answer

The answer of Arvin the Ant is on a picnic...

Question 2

I walk five miles in a straight line in a direction north of east,and I end up three miles east and several miles north.How many degrees north of east have I walked?
​
A) 37°
B) 45°
C) 31°
D) 53°
E) ​59°

Accepted Answer

The answer of I walk five miles in a straight...

Question 3

Vector Is 3.0 units in length and points along the positive x-axis;vector Is 8.0 units in length and points along a direction 150° from the positive x-axis.What is the magnitude of the resultant when vectors And Are added?
​
A) 7
B) 6.7
C) 10.7
D) 5.6
E) ​11

Accepted Answer

The answer of Vector Is 3.0 units in length and...

Question 4

A ball is rolled horizontally off a table with an initial speed of 0.28 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.33 s.What is the height of the table? (g = 9.8 m/s² and air resistance is negligible) A) 0.63 m B) 0.44 m C) 0.02 m D) 0.53 m E) 0.55 m

Accepted Answer

The correct answer is D.The height of the table can be calculated using the equation:h = (1/2) * g * t^2where:h is the height of the tableg is the acceleration due to gravity (9.8 m/s^2)t is the time it takes for the ball to fall from the table to the floorPlugging in the given values, we get:h = (1/2) * 9.8 m/s^2 * (0.33 s)^2h = 0.53 mTherefore, the height of the table is 0.53 m.

Question 5

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at shoulder level)by the catcher.At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)
A) just after leaving the center fielder's hand
B) just before arriving at the catcher's mitt
C) at the top of the trajectory
D) acceleration is constant during entire trajectory

Accepted Answer

The magnitude of acceleration is constant due to gravity, regardless of the ball's position in its trajectory.

Question 6

A string attached to an airborne kite is maintained at an angle of 49° with the horizontal.If a total of 170 m of string is reeled in while bringing the kite back to the ground,what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag. )
​
A) 128 m
B) 85 m
C) 32 m
D) 112 m
E) ​196 m

Accepted Answer

The answer of A string attached to an airborne kite...

Question 7

A ball is rolled horizontally off a table with an initial speed of 0.22 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.2 s.How far away from the table does the ball land? (g = 9.8 m/s² and air resistance is negligible) A) 0.24 m B) 0.044 m C) 0.392 m D) 0.152 m E) 0.088 m

Accepted Answer

The answer of A ball is rolled horizontally off a...

Question 8

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at an equal shoulder level)by the catcher.At what point is the ball's speed at a minimum? (air resistance is negligible)
A) just after leaving the center fielder's hand
B) just before arriving at the catcher's mitt
C) at the top of the trajectory
D) speed is constant during entire trajectory

Accepted Answer

According to the conservation of mechanical energy, when the baseball is at its highest point in the trajectory, all of its energy is in the form of potential energy and none of it is in the form of kinetic energy. Therefore, the speed of the ball is at a minimum at the top of its trajectory. The speed is greatest just after it leaves the center fielder's hand due to the transfer of kinetic energy from the fielder to the ball. From the top of the trajectory to just before arriving at the catcher's mitt, the speed decreases due to gravity, but it is still greater than the minimum speed at the top of the trajectory.

Question 9

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at shoulder level)by the catcher.At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible)
A) just after leaving the center fielder's hand
B) just before arriving at the catcher's mitt
C) at the top of the trajectory
D) magnitude of vertical component of velocity is constant

Accepted Answer

At the top of the trajectory, the ball has reached its maximum height and is momentarily at rest before it begins to descend. At this point, the vertical component of velocity is zero, meaning it has reached its minimum value.

Question 10

A helicopter is traveling at 50 m/s at a constant altitude of 100 m over a level field.If a wheel falls off the helicopter,with what speed will it hit the ground? (g = 9.8 m/s² and air resistance negligible) A) 59 m/s B) 45 m/s C) 67 m/s D) 4,460 m/s E) 57 m/s

Accepted Answer

The horizontal speed remains 50 m/s. The vertical speed upon impact can be calculated using the equation v = sqrt(2gh) = sqrt(2*9.8*100) = 44.3 m/s. The resultant speed is sqrt(50^2 + 44.3^2) = 67 m/s.

Question 11

Arvin the Ant travels 35 cm eastward,then 20 cm northward,and finally 10 cm westward.What is Arvin's direction of displacement with respect to his original position?
​
A) 39° N of E
B) 141° N of E
C) 51° N of W
D) 30° N of E
E) ​63° N of E

Accepted Answer

Arvin's net displacement is the vector sum of his three displacements. The first displacement is 35 cm eastward, the second displacement is 20 cm northward, and the third displacement is 10 cm westward. The net displacement is therefore:```(35 cm, 0 cm) + (0 cm, 20 cm) + (-10 cm, 0 cm) = (25 cm, 20 cm)```The magnitude of the net displacement is:```sqrt(25^2 + 20^2) = 32.02 cm```The direction of the net displacement is:```arctan(20 cm / 25 cm) = 39.81°```Therefore, Arvin's direction of displacement with respect to his original position is 39.81° N of E, which is closest to choice A, 39° N of E.

Question 12

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.1 m/s at an initial angle of 45° with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?
​
A) 21.6 m
B) 43.2 m
C) 64.8 m
D) 43.2 m.
E) 86.4 m

Accepted Answer

The maximum vertical displacement can be calculated using the formula: $ h = \frac{v^2 \sin^2(\theta)}{2g} $, where $ v = 29.1 \, \text{m/s} $, $ \theta = 45^\circ $, and $ g = 9.8 \, \text{m/s}^2 $. Plugging in the values, $ h = \frac{(29.1)^2 \times (\sin(45^\circ))^2}{2 \times 9.8} \approx 21.6 \, \text{m} $.

Question 13

Jack pulls a sled across a level field by exerting a force of 110 N at an angle of 30° with the ground.What are the parallel and perpendicular components,respectively,of this force with respect to the ground?​
A) 190 N,110 N
B) 110 N,190 N
C) 95 N,55 N
D) 55 N,95 N
E) ​64 N,191 N

Accepted Answer

To determine the parallel and perpendicular components of the force exerted by Jack, we can use trigonometry:

The parallel component is given by Fp = Fcosθ, where F is the magnitude of the force (110 N) and θ is the angle that the force makes with the ground (30°).

Fp = 110 N × cos 30° 
Fp = 110 N × 0.866 
Fp = 95 N

The perpendicular component is given by Fp = Fsinθ.

Fp = 110 N × sin 30° 
Fp = 110 N × 0.5 
Fp = 55 N

Therefore, the parallel component is 95 N and the perpendicular component is 55 N. The correct answer is C.

Question 14

John throws a baseball from the outfield from shoulder height,at an initial velocity of 29.7 m/s at an initial angle of 45.0° with respect to the horizontal.The ball is in its trajectory for a total interval of 4.00 s before the third baseman catches it at an equal shoulder-height level.(Assume air resistance negligible. )What is the ball's horizontal displacement?
​
A) 84 m
B) 168 m
C) 118.8 m
D) zero
E) 237.6 ​m

Accepted Answer

The horizontal displacement is given by:$$d = v_i * t * cos(theta)$$where:* v_i is the initial velocity* t is the time of flight* theta is the initial anglePlugging in the given values, we get:$$d = 29.7 m/s * 4.00 s * cos(45.0°) = 118.8 m$$Therefore, the correct answer is C) 118.8 m.

Question 15

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 28.1 m/s at an initial angle of 30.0° with respect to the horizontal.If it is in its trajectory for a total of 3.00 s before being caught by the third baseman at an equal shoulder-height level,what is the ball's net vertical displacement during its 3-s trajectory?
​
A) 73 m
B) 9.80 m
C) 10.1 m
D) zero
E) ​20.1 m

Accepted Answer

The net vertical displacement is zero because the ball is caught at the same height from which it was thrown.

Question 16

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 11.1 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.5 s.What is the height of the cliff? (g = 9.8 m/s² and air resistance is negligible) A) 179 m B) 148 m C) 118 m D) 31 m E) 137 m

Accepted Answer

The answer of A stone is thrown at an angle...

Question 17

A runner circles a track of radius 150 m in 150 s moving at a constant rate.If the runner was initially moving north,what has been the runner's average acceleration when halfway around the track? A) At a constant rate,the average acceleration would be zero. B) 6.28 m/s²,west C) 0.17 m/s²,south D) No answer is correct. E) 0.17 m/s²,east

Accepted Answer

The runner's average acceleration is given by the change in velocity divided by the time interval in which the change occurred. At the halfway point, the runner is moving horizontally to the east, so the change in velocity is the difference between the initial northward velocity and the final eastward velocity. Since the runner moves half the distance in half the time (i.e. 75 seconds), the average acceleration is (v_f - v_i) / t = (0 - (150 m/150 s)) / 75 s = -2 m/s^2 to the south. However, we need to take the magnitude of the acceleration, so the answer is 2 m/s^2 to the south, or approximately 0.17 m/s^2 to the south.

Question 18

Five boys are pushing on a snowball,and each is pushing with a force of 16.0 N.However,each boy is pushing in a different direction.They are pushing north,northeast,east,southeast,and south.(Each boy is pushing at an angle of 45.0° relative to his neighbor. )What is the magnitude of the total force on the ball?​
A) 0
B) 23 N
C) 38.6 N
D) 17.4 N
E) ​77.3 N

Accepted Answer

To solve this problem, we need to use vector addition. We can start by drawing a diagram with arrows representing the magnitude and direction of each boy's force. Each arrow will be 16.0 N long and at a 45-degree angle to its neighbors. Then, we can use the parallelogram rule to find the resultant force.

The resultant force is the diagonal of the parallelogram formed by the four forces. The magnitude of this diagonal can be found using the Pythagorean theorem, since the forces are all at 45-degree angles.

The length of one side of the parallelogram is 16.0 N, and the length of the other side is 32.0 N (since there are two forces at a 45-degree angle on each side). Using the Pythagorean theorem, we find that the magnitude of the resultant force is:

F = sqrt((16.0 N)^2 + (32.0 N)^2) = 38.6 N

Therefore, the magnitude of the total force on the ball is 38.6 N. The correct answer is (C).

Question 19

A jogger runs halfway around a circular path with a radius of 50 m.What,respectively,are the magnitude of the displacement and the distance jogged?
​
A) 50 m,157 m
B) 100 m,157 m
C) 0 m,314 m
D) 100 m,314 m
E) ​50 m,314 m

Accepted Answer

The displacement is the straight-line distance between the starting and ending points, which is the diameter of the circle (2 * radius = 100 m). The distance jogged is half the circumference of the circle (π * diameter = 157 m).

Question 20

VIs 3.0 units in length and points along the positive x-axis;
Is 7.0 units in length and points along a direction 150° from the positive x-axis.What is the direction of the resultant with respect to the positive x-axis?
​
A) 49°
B) 131°
C) 41°
D) 12°
E) ​168°

Accepted Answer

The answer of VIs 3.0 units in length and points...

Quiz 3: Vectors and Two-Dimensional Motion

Arvin the Ant is on a picnic table.He travels 35 cm eastward,then 20 cm northward,and finally 5 cm westward.What is the magnitude of Arvin's net displacement?

I walk five miles in a straight line in a direction north of east,and I end up three miles east and several miles north.How many degrees north of east have I walked?

Vector Is 3.0 units in length and points along the positive x-axis;vector Is 8.0 units in length and points along a direction 150° from the positive x-axis.What is the magnitude of the resultant when vectors And Are added?

A ball is rolled horizontally off a table with an initial speed of 0.28 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.33 s.What is the height of the table? (g = 9.8 m/s² and air resistance is negligible)

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher.At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)

A string attached to an airborne kite is maintained at an angle of 49° with the horizontal.If a total of 170 m of string is reeled in while bringing the kite back to the ground,what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag. )

A ball is rolled horizontally off a table with an initial speed of 0.22 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.2 s.How far away from the table does the ball land? (g = 9.8 m/s² and air resistance is negligible)

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at an equal shoulder level) by the catcher.At what point is the ball's speed at a minimum? (air resistance is negligible)

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher.At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible)

A helicopter is traveling at 50 m/s at a constant altitude of 100 m over a level field.If a wheel falls off the helicopter,with what speed will it hit the ground? (g = 9.8 m/s² and air resistance negligible)

Arvin the Ant travels 35 cm eastward,then 20 cm northward,and finally 10 cm westward.What is Arvin's direction of displacement with respect to his original position?

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.1 m/s at an initial angle of 45° with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?

Jack pulls a sled across a level field by exerting a force of 110 N at an angle of 30° with the ground.What are the parallel and perpendicular components,respectively,of this force with respect to the ground?

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 11.1 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.5 s.What is the height of the cliff? (g = 9.8 m/s² and air resistance is negligible)

A runner circles a track of radius 150 m in 150 s moving at a constant rate.If the runner was initially moving north,what has been the runner's average acceleration when halfway around the track?

A jogger runs halfway around a circular path with a radius of 50 m.What,respectively,are the magnitude of the displacement and the distance jogged?

VectorIs 3.0 units in length and points along the positive x-axis;vector Is 7.0 units in length and points along a direction 150° from the positive x-axis.What is the direction of the resultant with respect to the positive x-axis?

Quiz 3: Vectors and Two-Dimensional Motion

Arvin the Ant is on a picnic table.He travels 35 cm eastward,then 20 cm northward,and finally 5 cm westward.What is the magnitude of Arvin's net displacement? ​

I walk five miles in a straight line in a direction north of east,and I end up three miles east and several miles north.How many degrees north of east have I walked? ​

Vector Is 3.0 units in length and points along the positive x-axis;vector Is 8.0 units in length and points along a direction 150° from the positive x-axis.What is the magnitude of the resultant when vectors And Are added? ​

A ball is rolled horizontally off a table with an initial speed of 0.28 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.33 s.What is the height of the table? (g = 9.8 m/s2 and air resistance is negligible) ​

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher.At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)

A string attached to an airborne kite is maintained at an angle of 49° with the horizontal.If a total of 170 m of string is reeled in while bringing the kite back to the ground,what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag. ) ​

A ball is rolled horizontally off a table with an initial speed of 0.22 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.2 s.How far away from the table does the ball land? (g = 9.8 m/s2 and air resistance is negligible) ​

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at an equal shoulder level) by the catcher.At what point is the ball's speed at a minimum? (air resistance is negligible)

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher.At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible)

A helicopter is traveling at 50 m/s at a constant altitude of 100 m over a level field.If a wheel falls off the helicopter,with what speed will it hit the ground? (g = 9.8 m/s2 and air resistance negligible) ​

Arvin the Ant travels 35 cm eastward,then 20 cm northward,and finally 10 cm westward.What is Arvin's direction of displacement with respect to his original position? ​

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.1 m/s at an initial angle of 45° with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory? ​

Jack pulls a sled across a level field by exerting a force of 110 N at an angle of 30° with the ground.What are the parallel and perpendicular components,respectively,of this force with respect to the ground?​

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 11.1 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.5 s.What is the height of the cliff? (g = 9.8 m/s2 and air resistance is negligible) ​

A runner circles a track of radius 150 m in 150 s moving at a constant rate.If the runner was initially moving north,what has been the runner's average acceleration when halfway around the track? ​

A jogger runs halfway around a circular path with a radius of 50 m.What,respectively,are the magnitude of the displacement and the distance jogged? ​

VectorIs 3.0 units in length and points along the positive x-axis;vector Is 7.0 units in length and points along a direction 150° from the positive x-axis.What is the direction of the resultant with respect to the positive x-axis? ​