Fairgoers ride a Ferris wheel with a radius of 5.00 . The wheel completes one revolution every 33.0 .

If a rider accidentally drops a stuffed animal at the top of the wheel, where does it land relative to the base of the ride? (Note: The bottom of the wheel is 1.75 above the ground.)??

Please provide the units of your physical quantities. Is the radius in meters or feet? Is the revolution time in seconds or minutes?

Use the radius and rotation rate to get the horizontal velocity at the top of the rotation. Use the radius and height of the wheel to get time it takes the stuffed animal to fall.

To determine where the stuffed animal lands relative to the base of the ride, we need to find the vertical displacement of the stuffed animal when it is dropped at the top of the wheel.

Given:
Radius of the Ferris wheel, r = 5.00 m
Time for one revolution, T = 33.0 s
Height of the base of the wheel, h = 1.75 m

Step 1: Finding the circumference of the Ferris wheel
The circumference of a circle can be calculated using the formula C = 2πr.
Using the given radius, we can find:
C = 2π(5.00) ≈ 31.42 m

Step 2: Finding the vertical displacement during one revolution
During one revolution of the Ferris wheel, the rider moves around the circumference of the circle. This means that the vertical displacement is equal to the circumference of the wheel.

Vertical displacement = Circumference = 31.42 m

Step 3: Finding the vertical displacement during the time period T
To find the vertical displacement during the time period T, we need to calculate the fraction of the wheel's revolution completed during T.

Fraction of revolution completed = T / (time for one revolution)
Fraction of revolution completed = 33.0 / 33.0 = 1

Since the fraction of revolution completed is 1, the vertical displacement during T is equal to the vertical displacement for one revolution.

Vertical displacement during T = Vertical displacement during one revolution = 31.42 m

Step 4: Finding the landing point relative to the base of the ride
The stuffed animal is dropped at the top of the wheel, which means it will complete a full revolution before landing. The landing point can be determined by subtracting the height of the base from the vertical displacement during T.

Landing point = Vertical displacement during T - Height of the base
Landing point = 31.42 m - 1.75 m = 29.67 m

Therefore, the stuffed animal will land approximately 29.67 m below the top of the wheel, relative to the base of the ride.

To determine where the stuffed animal lands relative to the base of the ride, we need to understand the motion of the Ferris wheel.

The Ferris wheel completes one revolution every 33.0 seconds, which means it completes a full circle every 33.0 seconds.

The distance around the circumference of a circle is given by the formula C=2πr, where C is the circumference and r is the radius of the circle.

In this case, the radius of the Ferris wheel is given as 5.00 m. Therefore, the circumference of the Ferris wheel can be calculated as C=2π(5.00)=31.42 m.

Since the wheel takes 33.0 seconds to complete one revolution, we can divide the circumference by the time to find the linear velocity of a point on the wheel.

Linear velocity = Circumference / Time = 31.42 m / 33.0 s = 0.95 m/s.

Now, suppose the stuffed animal is dropped at the top of the wheel. The top of the wheel is at the maximum height, which is equal to the sum of the radius of the wheel (5.00 m) and the distance from the ground to the base of the wheel (1.75 m). So, the total height from the ground to the top of the wheel is 5.00 m + 1.75 m = 6.75 m.

As the stuffed animal falls, it will experience gravitational acceleration pulling it downward. The acceleration due to gravity is approximately 9.8 m/s².

Using the kinematic equation d = v0t + 0.5at², where d is the vertical displacement, v0 is the initial velocity, t is the time, and a is the acceleration, we can determine how far the stuffed animal falls during the time it takes for the Ferris wheel to complete one revolution.

In this case, the initial velocity v0 is 0 m/s (since the stuffed animal is initially at rest at the top of the wheel), the time t is 33.0 seconds (the time for one revolution), the acceleration a is -9.8 m/s² (negative because it is acting in the opposite direction to the displacement), and we want to solve for the vertical displacement d.

Using the equation, we have d = 0.5(-9.8)(33.0)² = -5,313 m²/s².

Since the displacement is negative, it means the stuffed animal falls downward. To find where it lands relative to the base of the ride, we need to subtract the vertical displacement from the total height from the ground to the top of the wheel.

Landing position = Total height - Vertical displacement = 6.75 m - (-5,313 m²/s²) = 6.75 m + 5,313 m²/s².

So, the stuffed animal will land approximately 5,320.75 meters below the total height of the wheel or approximately 5,314 meters below the top of the wheel relative to the base of the ride.