Question 1

Vector  is 3.0 units in length and points along the positive x-axis;vector  is 4.0 units in length and points along a direction 150 $\degree$from the positive x-axis.What is the magnitude of the resultant when vectors  and  are added?

Accepted Answer

The answer of Vector  is 3.0 units in length...

Question 2

Arvin the Ant is on a picnic table.He travels 30 cm eastward,then 25 cm northward,and finally 15 cm westward.What is the magnitude of Arvin's net displacement?

Accepted Answer

Arvin's net displacement can be found using the Pythagorean theorem. He ends up 15 cm east (30 cm east - 15 cm west) and 25 cm north. The net displacement is the hypotenuse of a right triangle with these sides: √(15² + 25²) = √(225 + 625) = √850 ≈ 29 cm.

Question 3

Arvin the Ant travels 30 cm eastward,then 25 cm northward,and finally 15 cm westward.What is Arvin's direction of displacement with respect to his original position?

Accepted Answer

The answer of Arvin the Ant travels 30 cm eastward,then...

Question 4

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.30 s.What is the height of the table? (g = 9.8 m/s² and air resistance is negligible)

Accepted Answer

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

Question 5

A string attached to an airborne kite is maintained at an angle of 40 $\degree$ with the horizontal.If a total of 120 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. )

Accepted Answer

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

Question 6

Five boys are pushing on a snowball,and each is pushing with a force of 10.0 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 $\degree$relative to his neighbor. )What is the magnitude of the total force on the ball?

Accepted Answer

Since the forces are all at 45 degrees to each other, we can use vector addition to find the total force.

First, we can find the horizontal and vertical components of each force using trigonometry. Since they are all the same magnitude, each force has a component of 10.0 N cos(45°) = 7.07 N in the horizontal direction, and a component of 10.0 N sin(45°) = 7.07 N in the vertical direction.

Next, we can add up all the horizontal components and all the vertical components separately to get the total horizontal and vertical components of the force.

Total horizontal force = (7.07 N + 7.07 N + 10.0 N + 7.07 N - 7.07 N) = 24.1 N to the right
Total vertical force = (7.07 N + 10.0 N + 7.07 N - 7.07 N - 7.07 N) = 10.0 N up

Finally, we can use the Pythagorean theorem to find the magnitude of the total force:

Total force = sqrt((24.1 N)^2 + (10.0 N)^2) = 27.1 N

So the answer is (C) 24.1 N.

Question 7

A helicopter is traveling at 40 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)

Accepted Answer

The horizontal velocity of the helicopter does not affect the vertical acceleration of the wheel due to gravity. Therefore, the only force acting on the wheel is its weight, given by mg, where m is the mass of the wheel and g is the acceleration due to gravity. The initial vertical velocity of the wheel is zero. Using the equation of motion, h = ut + 1/2 gt^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time, we can find the time it takes for the wheel to hit the ground.

h = ut + 1/2 gt^2 
100 = 0t + 1/2 (9.8) t^2 
t = sqrt(100/4.9)

t ≈ 6.43 seconds

Using the equation, v = gt, where v is the final velocity, g is the acceleration due to gravity, and t is the time, we can find the final velocity of the wheel.

v = gt 
v = 9.8 x 6.43 
v ≈ 63 m/s

Therefore, the wheel will hit the ground with a speed of approximately 63 m/s, which is closest to option C) 60 m/S.

Question 8

A stone is thrown at an angle of 30 $\degree$ above the horizontal from the top edge of a cliff with an initial speed of 12 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.6 s.What is the height of the cliff? (g = 9.8 m/s² and air resistance is negligible)

Accepted Answer

We can use the kinematic equations of motion to solve this problem.

First, we need to find the vertical component of the initial velocity:

v0y = v0sinθ = 12sin30° = 6 m/s

Using the kinematic equation:

Δy = v0yt + 0.5at^2

where Δy is the height of the cliff, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight (5.6 s), we can solve for Δy:

Δy = v0yt + 0.5at^2 = 6(5.6) + 0.5(-9.8)(5.6)^2 = 120.96 m

So the height of the cliff is approximately 120 m (to two significant figures). Therefore, the correct answer is C.

Question 9

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30.0 $\degree$ with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?

Accepted Answer

The maximum vertical displacement can be calculated using the formula: $ h = \frac{v^2 \sin^2(\theta)}{2g} $, where $ v = 29.4 \, \text{m/s} $, $ \theta = 30^\circ $, and $ g = 9.8 \, \text{m/s}^2 $. Plugging in the values, $ h = \frac{(29.4)^2 \times \sin^2(30^\circ)}{2 \times 9.8} = 11.0 \, \text{m} $.

Question 10

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)

Accepted Answer

At the top of the trajectory, the ball reaches its maximum height and momentarily stops moving vertically, meaning the vertical component of velocity is momentarily zero. Therefore, the magnitude of the vertical component of velocity is at its minimum value at this point.

Question 11

A jogger runs halfway around a circular path with a radius of 60 m.What,respectively,are the magnitude of the displacement and the distance jogged?

Accepted Answer

The displacement is the straight line distance between the start and end points, which is the diameter of the circle (2 * radius = 120 m). The distance jogged is half the circumference of the circle (π * diameter = 188 m).

Question 12

A runner circles a track of radius 100 m in 100 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?

Accepted Answer

The runner's average acceleration is calculated by the change in velocity over time. Halfway around the track, the runner's direction changes from north to south. The speed remains constant, so the change in velocity is twice the speed directed south. The average acceleration is this change in velocity divided by the time taken (50 s), resulting in 0.25 m/s² directed south.

Question 13

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30.0 $\degree$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?

Accepted Answer

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

Question 14

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)

Accepted Answer

The acceleration of the baseball is constant due to the absence of air resistance. Therefore, the magnitude of the acceleration is the same at all points during the trajectory.

Question 15

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

Accepted Answer

To find the angle north of east, we need to draw a right triangle with the hypotenuse representing the distance walked (6 miles), the adjacent side representing the distance walked east (2 miles), and the opposite side representing the distance walked north (unknown). We can use the trigonometric function tangent to find the angle opposite the north side.

tan θ = opposite/adjacent 
tan θ = (distance walked north) / 2 
θ = arctan ((distance walked north) / 2)

From the problem, we know that the distance walked north is several miles (let's call it x). So, we have:

θ = arctan (x/2)

Using the Pythagorean theorem, we can solve for x:

6^2 = 2^2 + x^2 
x = √32

So,

θ = arctan (√32 / 2)

Using a calculator, we find that θ ≈ 71.57 degrees. Rounding to the nearest degree, we get 72 degrees, which is closest to answer choice D, 71°F.

Question 16

John throws a baseball from the outfield from shoulder height,at an initial velocity of 29.4 m/s at an initial angle of 30.0 $\degree$ with respect to the horizontal.The ball is in its trajectory for a total interval of 3.00 s before the third baseman catches it at an equal shoulder-height level.(Assume air resistance negligible. )What is the ball's horizontal displacement?

Accepted Answer

The horizontal displacement can be calculated using the formula: horizontal velocity = initial velocity * cos(angle). The horizontal velocity is 29.4 m/s * cos(30°) = 25.5 m/s. The horizontal displacement is then horizontal velocity * time = 25.5 m/s * 3.00 s = 76.5 m, which is approximately 76.4 m.

Question 17

Vector  is 3.0 units in length and points along the positive x-axis;vector  is 4.0 units in length and points along a direction 150 $\degree$from the positive x-axis.What is the direction of the resultant with respect to the positive x-axis?

Accepted Answer

To find the direction of the resultant, we need to first calculate the angle that vector 11eaa64f_8f76_3f9a_a696_bdf9d35c511c_TB5258_11 makes with the positive x-axis:

angle = 150 degrees - 180 degrees = -30 degrees

Note that we subtract 180 degrees from 150 degrees because the angle is measured clockwise from the positive x-axis.

Next, we can use the cosine law to find the angle between the resultant and the positive x-axis:

cos(theta) = (3^2 + 4^2 - 2(3)(4)cos(-30 degrees)) / (2(3)(4))

cos(theta) = 0.9167

theta = cos^-1(0.9167) = 22.6 degrees

Finally, because the angle between vector 11eaa64f_8f76_3f99_a696_038fe9b42aa9_TB5258_11 and the positive x-axis is 0 degrees, the direction of the resultant with respect to the positive x-axis is:

22.6 degrees - 0 degrees = 22.6 degrees

Therefore, the answer is D) 103 degrees.

Question 18

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.30 s.How far away from the table does the ball land? (g = 9.8 m/s² and air resistance is negligible)

Accepted Answer

The horizontal distance can be calculated using the formula: distance = speed × time. Here, distance = 0.24 m/s × 0.30 s = 0.072 m.

Question 19

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

Accepted Answer

The answer of Jack pulls a sled across a level...

Question 20

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)

Accepted Answer

According to the laws of projectile motion, the speed of a projectile is at a minimum at the highest point of its trajectory. Therefore, the ball's speed is at a minimum at the top of its trajectory, which is the answer choice C.

Quiz 3: Vectors and Two-Dimensional Motion

Arvin the Ant is on a picnic table.He travels 30 cm eastward,then 25 cm northward,and finally 15 cm westward.What is the magnitude of Arvin's net displacement?

Arvin the Ant travels 30 cm eastward,then 25 cm northward,and finally 15 cm westward.What is Arvin's direction of displacement with respect to his original position?

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.30 s.What is the height of the table? (g = 9.8 m/s² and air resistance is negligible)

A string attached to an airborne kite is maintained at an angle of 40 $\degree$ with the horizontal.If a total of 120 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 helicopter is traveling at 40 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 stone is thrown at an angle of 30 $\degree$ above the horizontal from the top edge of a cliff with an initial speed of 12 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.6 s.What is the height of the cliff? (g = 9.8 m/s² and air resistance is negligible)

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30.0 $\degree$ with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?

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 jogger runs halfway around a circular path with a radius of 60 m.What,respectively,are the magnitude of the displacement and the distance jogged?

A runner circles a track of radius 100 m in 100 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 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)

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

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.30 s.How far away from the table does the ball land? (g = 9.8 m/s² and air resistance is negligible)

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

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)

Quiz 3: Vectors and Two-Dimensional Motion

Vector is 3.0 units in length and points along the positive x-axis;vector is 4.0 units in length and points along a direction 150 °\degree° from the positive x-axis.What is the magnitude of the resultant when vectors and are added?

Arvin the Ant is on a picnic table.He travels 30 cm eastward,then 25 cm northward,and finally 15 cm westward.What is the magnitude of Arvin's net displacement?

Arvin the Ant travels 30 cm eastward,then 25 cm northward,and finally 15 cm westward.What is Arvin's direction of displacement with respect to his original position?

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.30 s.What is the height of the table? (g = 9.8 m/s2 and air resistance is negligible)

A string attached to an airborne kite is maintained at an angle of 40 °\degree° with the horizontal.If a total of 120 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 helicopter is traveling at 40 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 baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30.0 °\degree° with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?

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 jogger runs halfway around a circular path with a radius of 60 m.What,respectively,are the magnitude of the displacement and the distance jogged?

A runner circles a track of radius 100 m in 100 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 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)

I walk six miles in a straight line in a direction north of east,and I end up two 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 4.0 units in length and points along a direction 150 °\degree° from the positive x-axis.What is the direction of the resultant with respect to the positive x-axis?

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.30 s.How far away from the table does the ball land? (g = 9.8 m/s2 and air resistance is negligible)

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

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 ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.30 s.What is the height of the table? (g = 9.8 m/s² and air resistance is negligible)

A string attached to an airborne kite is maintained at an angle of 40 $\degree$ with the horizontal.If a total of 120 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 helicopter is traveling at 40 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 baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30.0 $\degree$ with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.30 s.How far away from the table does the ball land? (g = 9.8 m/s² and air resistance is negligible)

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