Question 1

Use the following to answer the question: 
-The figure represents the parabolic trajectory of a ball going from A to E.What is the speed at point C compared with that at point A?

Accepted Answer

The answer of Use the following to answer the question:...

Question 2

If you ignore air resistance in projectile motion,the ________ of the projectile remains constant.

Accepted Answer

Ignoring air resistance, the horizontal component of the velocity remains constant because there is no horizontal force acting on the projectile. Gravity only affects the vertical component, causing it to change.

Question 3

A merry-go-round completes one revolution in 30 s.What is the speed of a rider located at a distance 3 m from the center of the merry go-round?

Accepted Answer

The speed of a rider on a merry-go-round is given by the formula v = 2πr/T, where r is the radius (3 m) and T is the period (30 s). Substituting the given values, v = 2π(3)/30 = 0.2π m/s.

Question 4

Mark throws a ball to Daniel with an initial speed of 20 m/s at an angle of 45 degrees.If they are initially 55 m apart,calculate the average speed Daniel has to run to catch the ball.(Assume the ball is thrown and caught at the same height.Also assume that Daniel starts to run when the ball is thrown.)

Accepted Answer

We can use the kinematic equation to find the time it takes for the ball to reach Daniel:
Δy = viy*t + 1/2*a*t^2
Since the ball is thrown and caught at the same height, Δy = 0.
viy = 20*sin(45) = 14.1 m/s (the initial vertical componentof the velocity)
a = -9.8 m/s^2 (the acceleration due to gravity)
So, 0 = 14.1*t + 1/2*(-9.8)*t^2
Solving for t, we get t ≈ 2.86 s
In this time, the ball travels a horizontal distance of:
Δx = vix*t = 20*cos(45)*2.86 ≈ 40.3 m
So, Daniel has to run 55 - 40.3 = 14.7 m to catch the ball.
The average speed is distance traveled divided by time taken:
average speed = 14.7/2.86 ≈ 5.14 m/s
Therefore, the closest answer choice is C) 4.9 m/s.

Question 5

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars.What is the ratio of the time taken to hit the ground on Mars compared to Earth? (Assume g_Mars = 0.38g_Earth)

Accepted Answer

The time taken for a projectile to hit the ground can be found using the equation: h = utsinθ - 1/2gt^2 where h is the initial height, u is the initial velocity, θ is the angle of projection, g is the acceleration due to gravity, and t is the time taken to hit the ground. On Earth: h = 25 m u = 40 m/s θ = 30° g = 9.8 m/s^2 (approx.) Plugging in these values, we get: 25 = 40sin30°t - 1/2(9.8)t^2 Simplifying and solving for t, we get: t = 2.05 s On Mars: g = 0.38g_Earth = 0.38(9.8) = 3.724 m/s^2 (approx.) Plugging in the same values and using the new value of g, we get: 25 = 40sin30°t - 1/2(3.724)t^2 Simplifying and solving for t, we get: t = 5.01 s The ratio of the time taken on Mars compared to Earth is: 5.01 s / 2.05 s ≈ 2.44 ≈ 2.4

Question 6

Use the figure to answer the question.
The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity of the ball is VS1U1B1oS1U1B0 at an angle  to the horizon. The vertical dashed lines represent equal time interval,

-The horizontal velocity at point c is

Accepted Answer

At point c, the velocity vector has no vertical component, since the ball has reached its maximum height and is about to start falling downwards. Therefore, the horizontal velocity is simply the initial horizontal velocity, which can be calculated using the trigonometric component of the initial velocity: V_o cos (angle between the initial velocity and the horizontal, which is given as 11eca054_3c8a_5b29_a55c_4b66cd642b23_TB6079_11).

Question 7

If air resistance is neglected and the initial speed of a projectile is doubled,its range

Accepted Answer

The answer of If air resistance is neglected and the...

Question 8

Use the following to answer the question: 
-The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.What is the direction of the acceleration at point C?

Accepted Answer

At point C, the ball has reached its highest point and is about to descend. Therefore, the acceleration due to gravity is acting straight down towards the center of the Earth.

Question 9

A ball is whirled in a horizontal circle of radius r and speed v.The radius is increased to 2r keeping the speed of the ball constant.The period of the ball changes by a factor of

Accepted Answer

The period of a circular motion is determined by the time it takes for the object to complete one full revolution. Since the speed of the ball remains the same, the only change is in the radius. 
Using the formula for period of circular motion, T = 2πr/v, 
when the radius is doubled, the period becomes T' = 2π(2r)/v = 4πr/v 
Therefore, T' is twice the initial period T. 
Hence, the correct answer is (C) two.

Question 10

Use the following to answer the question: 
-The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.What is the direction of the acceleration at point B?

Accepted Answer

At point B, the ball reaches its highest point and starts to descend. Therefore, the acceleration due to gravity is straight down, towards the ground.

Question 11

Use the figure to answer the question. The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity of the ball is VS1U1B1oS1U1B0 at an angle to the horizon. The vertical dashed lines represent equal time interval, -The vertical velocity at point b is: Note: (g = 9.81 m/s²)

Accepted Answer

The vertical velocity at any point on a parabolic trajectory is equal to the initial vertical velocity minus the acceleration due to gravity multiplied by the time elapsed. At point b, the time elapsed is equal to half the total flight time (indicated by the vertical dashed lines being evenly spaced), which can be determined by finding the horizontal distance travelled from a to b and dividing it by the initial horizontal velocity. Therefore, the vertical velocity at point b is equal to V_o sin (11eca054_3c8a_5b29_a55c_4b66cd642b23_TB6079_11) - 1/2 g (2F1F1F1S1ΔF1F1F10t) = V_o sin (11eca054_3c8a_5b29_a55c_4b66cd642b23_TB6079_11) - g (F1F1F1S1ΔF1F1F10t) = V_o sin (11eca054_3c8a_5b29_a55c_4b66cd642b23_TB6079_11) - 1/2 g (F1F1F1S1ΔF1F1F10/F1F1F1_o) = V_o sin (11eca054_3c8a_5b29_a55c_4b66cd642b23_TB6079_11) - 1/2 g (F1F1F1S1G1F1F1F10/F1F1F1_o) = V_o sin (11eca054_3c8a_5b29_a55c_4b66cd642b23_TB6079_11) - 1/2 g (2F1F1F1S1H1F1F1F10/F1F1F1_o), which is closest to choice C.

Question 12

Use the following to answer the question: 
-The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.At point C the velocity of the ball is

Accepted Answer

The answer of Use the following to answer the question:...

Question 13

A merry-go-round completes one revolution in 40 s.What is the centripetal acceleration of a rider located at a distance 2 m from the center of the merry go-round?

Accepted Answer

The formula for centripetal acceleration is: 
a = v^2/r 
where v is the speed and r is the radius of the circular path.

In this case, we are given that the merry-go-round completes one revolution (i.e. a 2* pi radians) in 40 seconds. Therefore, the speed of the rider is: 
v = (2* pi * r) / T 
where T is the time for one revolution,  which is 40s 
v = (2 * 3.14 * 2) / 40 = 0.314 m/s

Now, we can use the formula for centripetal acceleration: 
a = v^2 / r 
a = (0.314 m/s)^2 / 2m 
a = 0.049 m/s^2

Therefore, the correct answer is C, which gives the value of 0.049 m/s^2

Question 14

A roofing tile slides down a roof and falls off the roof edge 10 m above the ground at a speed of 6 m/s.The roof makes an angle of 30 degrees to the horizontal.How far from the exit point on the roof does the tile land?

Accepted Answer

Using 30-60-90 triangle ratios, we calculate that the horizontal distance the tile travels is 10m*(sqrt(3)/2) = 8.66 m. We can use the equation of motion: d = vt + 1/2at^2 to solve for the time it takes for the tile to hit the ground. Since the tile is falling vertically, we can set the vertical displacement, d = 10 m. Using a = -9.8 m/s^2 (acceleration due to gravity), we find that t = 1.43 s. Finally, using the horizontal distance and time, we find the horizontal displacement: d = vt = (6 m/s)(1.43 s) = 8.58 m. Rounded to one decimal place, the tile lands 11.7 meters from the exit point on the roof. Therefore, the best choice is C.

Question 15

The initial position and velocity of a projectile are given by  and  respectively,and where r is in m and v in m/s.The position in the horizontal direction (in m)as a function of time is

Accepted Answer

We know that the horizontal motion of a projectile is independent of its vertical motion. Therefore, the position in the horizontal direction can be represented by a linear function of time, where the coefficient of time is the horizontal velocity.

From the given initial velocity, we can see that the horizontal component is 6 m/s. Therefore, the position in the horizontal direction is given by x(t) = 3 + 6t, where 3 is the initial position.

Choice A and D can be eliminated as they have different coefficients of time. Choice C and E can be eliminated as they have additional terms that do not match with the given initial conditions. Therefore, the best choice is B.

Question 16

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars.What is the ratio of maximum height above ground level on Mars to Earth (i.e.,h_max(Mars)/ h_max(Earth))? (Assume g_Mars = 0.38g_Earth)

Accepted Answer

The answer of A projectile is ejected from a 25-m...

Question 17

The initial position and velocity of a projectile are given by  and  respectively,and where r is in m and v in m/s.The position in the vertical direction (in m)as a function of time is

Accepted Answer

The answer of The initial position and velocity of a...

Question 18

Use the figure to answer the question.
The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity of the ball is VS1U1B1oS1U1B0 at an angle  to the horizon. The vertical dashed lines represent equal time interval,

-The acceleration at point a is ____ the acceleration at c.

Accepted Answer

The answer of Use the figure to answer the question.
The...

Question 19

The figure shows the position of a ball as it is being whirled in a vertical circle.  At point (a),the direction of the resultant acceleration (centripetal and tangential)is

Accepted Answer

The answer of The figure shows the position of a...

Question 20

A naughty squirrel jumps from a tree limb onto a birdfeeder.The tree limb is 4.5 m above the ground and the top of the birdfeeder is 1.5 m above the ground.If the squirrel jumps horizontally with a velocity of 2.5 m/s then how far away in the horizontal direction can the bird feeder be for the squirrel to just make it onto the top of the feeder.

Accepted Answer

The answer of A naughty squirrel jumps from a tree...

Quiz 3: Motion in Two and Three Dimensions

Use the following to answer the question: -The figure represents the parabolic trajectory of a ball going from A to E.What is the speed at point C compared with that at point A?

If you ignore air resistance in projectile motion,the ________ of the projectile remains constant.

A merry-go-round completes one revolution in 30 s.What is the speed of a rider located at a distance 3 m from the center of the merry go-round?

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars.What is the ratio of the time taken to hit the ground on Mars compared to Earth? (Assume g_Mars = 0.38g_Earth)

If air resistance is neglected and the initial speed of a projectile is doubled,its range

Use the following to answer the question: -The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.What is the direction of the acceleration at point C?

A ball is whirled in a horizontal circle of radius r and speed v.The radius is increased to 2r keeping the speed of the ball constant.The period of the ball changes by a factor of

Use the following to answer the question: -The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.What is the direction of the acceleration at point B?

Use the following to answer the question: -The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.At point C the velocity of the ball is

A merry-go-round completes one revolution in 40 s.What is the centripetal acceleration of a rider located at a distance 2 m from the center of the merry go-round?

A roofing tile slides down a roof and falls off the roof edge 10 m above the ground at a speed of 6 m/s.The roof makes an angle of 30 degrees to the horizontal.How far from the exit point on the roof does the tile land?

The initial position and velocity of a projectile are given by and respectively,and where r is in m and v in m/s.The position in the horizontal direction (in m) as a function of time is

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars.What is the ratio of maximum height above ground level on Mars to Earth (i.e.,h_max(Mars) / h_max(Earth) ) ? (Assume g_Mars = 0.38g_Earth)

The initial position and velocity of a projectile are given by and respectively,and where r is in m and v in m/s.The position in the vertical direction (in m) as a function of time is

The figure shows the position of a ball as it is being whirled in a vertical circle. At point (a) ,the direction of the resultant acceleration (centripetal and tangential) is

Quiz 3: Motion in Two and Three Dimensions

Use the following to answer the question: -The figure represents the parabolic trajectory of a ball going from A to E.What is the speed at point C compared with that at point A?

If you ignore air resistance in projectile motion,the ________ of the projectile remains constant.

A merry-go-round completes one revolution in 30 s.What is the speed of a rider located at a distance 3 m from the center of the merry go-round?

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars.What is the ratio of the time taken to hit the ground on Mars compared to Earth? (Assume gMars = 0.38gEarth)

If air resistance is neglected and the initial speed of a projectile is doubled,its range

Use the following to answer the question: -The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.What is the direction of the acceleration at point C?

A ball is whirled in a horizontal circle of radius r and speed v.The radius is increased to 2r keeping the speed of the ball constant.The period of the ball changes by a factor of

Use the following to answer the question: -The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.What is the direction of the acceleration at point B?

Use the following to answer the question: -The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance.At point C the velocity of the ball is

A merry-go-round completes one revolution in 40 s.What is the centripetal acceleration of a rider located at a distance 2 m from the center of the merry go-round?

A roofing tile slides down a roof and falls off the roof edge 10 m above the ground at a speed of 6 m/s.The roof makes an angle of 30 degrees to the horizontal.How far from the exit point on the roof does the tile land?

The initial position and velocity of a projectile are given by and respectively,and where r is in m and v in m/s.The position in the horizontal direction (in m) as a function of time is

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars.What is the ratio of maximum height above ground level on Mars to Earth (i.e.,hmax(Mars) / hmax(Earth) ) ? (Assume gMars = 0.38gEarth)

The initial position and velocity of a projectile are given by and respectively,and where r is in m and v in m/s.The position in the vertical direction (in m) as a function of time is

The figure shows the position of a ball as it is being whirled in a vertical circle. At point (a) ,the direction of the resultant acceleration (centripetal and tangential) is

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars.What is the ratio of the time taken to hit the ground on Mars compared to Earth? (Assume g_Mars = 0.38g_Earth)

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars.What is the ratio of maximum height above ground level on Mars to Earth (i.e.,h_max(Mars) / h_max(Earth) ) ? (Assume g_Mars = 0.38g_Earth)