Question 1

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What should be the radius of the path that leads to same centripetal acceleration while it travels at speed 2V?

Accepted Answer

Centripetal acceleration is given by a_c = V²/R. If the speed is doubled to 2V, the new centripetal acceleration becomes (2V)²/R' = 4V²/R'. To maintain the same centripetal acceleration, R' must be 4R.

Question 2

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 3

An object traveling in a circle at a variable speed

Accepted Answer

The object traveling in a circle at a variable speed experiences a tangential acceleration (A) because its speed changes as it moves around the circle. It also experiences a centripetal acceleration (B) because there is a force acting towards the center of the circle that is necessary for the object to continue moving in a circle. Finally, the object has a velocity directed along the tangent (C) because it is moving in a circular path and its velocity is always tangent to the circle at any given point. Therefore, all of the above statements are true and the best choice is D.

Question 4

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 bird feeder 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...

Question 5

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What is its acceleration if it goes around a curve of radius 3R at a speed of 2V?

Accepted Answer

The centripetal acceleration is given by a_c= V^2/R. If the car goes around a curve of radius 3R at a speed of 2V, the centripetal acceleration is (2V)^2/(3R) = 4V^2/(3R). Dividing this by V^2/R gives (4V^2/(3R)) / (V^2/R) = 4/3, so the acceleration is multiplied by a factor of 4/3. Thus the answer is B, 4/3)a_c.

Question 6

When a particle moves in a circle with constant speed, its acceleration is

Accepted Answer

When a particle moves in a circle with constant speed, it experiences centripetal acceleration, which is constant in magnitude but changes direction as the particle moves around the circle.

Question 7

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

Accepted Answer

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

Question 8

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 9

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What should be the radius of the path that leads to twice the centripetal acceleration while it travels at the same speed V?

Accepted Answer

Centripetal acceleration is given by $ a_c = \frac{V^2}{R} $. To double the centripetal acceleration while keeping the speed constant, the radius must be halved, so the new radius is $ \frac{R}{2} $.

Question 10

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

Accepted Answer

The range of a projectile is proportional to the square of its initial velocity, so if the initial speed is doubled, the range will increase by a factor of four.

Question 11

An airplane in a horizontal flight releases a relief package that travels along possible paths as suggested in the diagram.  The trajectory of the package is best represented by

Accepted Answer

The answer of An airplane in a horizontal flight releases...

Question 12

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

Accepted Answer

The range of a projectile is directly proportional to the square of its initial velocity. If the initial speed is halved, it becomes 1/4 of the original value, so the range will be 1/16 of the original range, or decreased by a factor of four.

Question 13

An object traveling in a circle at constant speed

Accepted Answer

An object traveling in a circle at constant speed experiences an acceleration toward the center of the circle. This is known as centripetal acceleration, and it is directed perpendicular to the velocity of the object, toward the center of the circle. Despite the acceleration, the object's speed remains constant because the direction of motion is constantly changing. Therefore, choices A, B, and C are false.

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

We can use the kinematic equation to find the horizontal distance traveled by the tile.

Δx = v0x * t + 1/2 * a * t^2

Since there is no horizontal acceleration, a = 0.

But we need to find t first.

We know that vf = 0 at the highest point, so we can use the equation vf^2 = v0^2 + 2*a*Δy, where Δy = 10 m and v0 = 6 m/s.

0 = (6 m/s)^2 + 2*a*(10 m)
a = -18 m/s^2 (acceleration is down)

Now we can use the equation Δy = v0y * t + 1/2 * a * t^2 to find t.

10 m = v0y * t + 1/2 * (-18 m/s^2) * t^2
10 m = (6 m/s) * sin(30°) * t - 9 m/s^2 * t^2
0 = 3t^2 - 2t - 10/9
t = 1.58 s (we only use the positive root here)

Now we can use our first equation to find the horizontal distance traveled:

Δx = v0x * t + 1/2 * a * t^2
Δx = (6 m/s) * cos(30°) * (1.58 s)
Δx = 11.7 m

Therefore, the tile lands 11.7 m from the exit point on the roof.

Quiz 3: Motion in Two and Three Dimensions

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What should be the radius of the path that leads to same centripetal acceleration while it travels at speed 2V?

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) .

An object traveling in a circle at a variable speed

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What is its acceleration if it goes around a curve of radius 3R at a speed of 2V?

When a particle moves in a circle with constant speed, its acceleration is

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

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What should be the radius of the path that leads to twice the centripetal acceleration while it travels at the same speed V?

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

An airplane in a horizontal flight releases a relief package that travels along possible paths as suggested in the diagram. The trajectory of the package is best represented by

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

An object traveling in a circle at constant speed

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?

Quiz 3: Motion in Two and Three Dimensions

A car going around a curve of radius R at a speed V experiences a centripetal acceleration ac. What should be the radius of the path that leads to same centripetal acceleration while it travels at speed 2V?

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) .

An object traveling in a circle at a variable speed

A car going around a curve of radius R at a speed V experiences a centripetal acceleration ac. What is its acceleration if it goes around a curve of radius 3R at a speed of 2V?

When a particle moves in a circle with constant speed, its acceleration is

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

A car going around a curve of radius R at a speed V experiences a centripetal acceleration ac. What should be the radius of the path that leads to twice the centripetal acceleration while it travels at the same speed V?

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

An airplane in a horizontal flight releases a relief package that travels along possible paths as suggested in the diagram. The trajectory of the package is best represented by

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

An object traveling in a circle at constant speed

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?

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What should be the radius of the path that leads to same centripetal acceleration while it travels at speed 2V?

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 car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What is its acceleration if it goes around a curve of radius 3R at a speed of 2V?

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c. What should be the radius of the path that leads to twice the centripetal acceleration while it travels at the same speed V?