A ferris wheel makes one rotation in 15 minutes. Find your car's location and the angle of rotation after: 3 mins., 5 mins., 9 mins., 12 mins. The diameter of the wheel is 328 ft. and the height, with the base, is 369 ft.

3 min - 2•π/5 (rad) = 72º,

5 min - 2•π/3 (rad) = 120º,
12 min - 2•π•12/15 (rad) =288 º

Thank you Elena. I really appreciate your halp.

To find the car's location and the angle of rotation after a given time on a ferris wheel, we need to use the concepts of circumference and angular displacement.

We know that the ferris wheel makes one rotation in 15 minutes, which means it completes a full circle. The circumference of a circle can be calculated using the formula C = πd, where C represents the circumference and d represents the diameter.

Given the diameter of the wheel is 328 ft, the circumference can be calculated as follows:
C = π * 328 = 1030.52 ft.

Now, let's find the car's location and the angle of rotation at different times:

1. After 3 minutes:
Since the ferris wheel takes 15 minutes to complete one rotation, the fraction of the rotation completed in 3 minutes can be calculated as 3/15 = 1/5. To find the distance travelled by the car, we multiply this fraction by the circumference of the wheel:
Distance = (1/5) * 1030.52 = 206.1 ft.

The car's location after 3 minutes is 206.1 ft from the starting point. To find the angle of rotation, we can use the formula ∠ = (Distance / Circumference) * 360 degrees:
∠ = (206.1 / 1030.52) * 360 = 71.6 degrees.

Therefore, after 3 minutes, the car is located 206.1 ft from the starting point, and the angle of rotation is 71.6 degrees.

2. After 5 minutes:
Similar to the previous step, the fraction of the rotation completed in 5 minutes is 5/15 = 1/3. Using this fraction, we can calculate the distance travelled by the car:
Distance = (1/3) * 1030.52 = 343.5 ft.

The car's location after 5 minutes is 343.5 ft from the starting point. To find the angle of rotation:
∠ = (343.5 / 1030.52) * 360 = 120.0 degrees.

Therefore, after 5 minutes, the car is located 343.5 ft from the starting point, and the angle of rotation is 120.0 degrees.

3. After 9 minutes:
The fraction of the rotation completed in 9 minutes is 9/15 = 3/5. Using this fraction, we can calculate the distance travelled by the car:
Distance = (3/5) * 1030.52 = 618.3 ft.

The car's location after 9 minutes is 618.3 ft from the starting point. To find the angle of rotation:
∠ = (618.3 / 1030.52) * 360 = 216.0 degrees.

Therefore, after 9 minutes, the car is located 618.3 ft from the starting point, and the angle of rotation is 216.0 degrees.

4. After 12 minutes:
The fraction of the rotation completed in 12 minutes is 12/15 = 4/5. Using this fraction, we can calculate the distance travelled by the car:
Distance = (4/5) * 1030.52 = 824.4 ft.

The car's location after 12 minutes is 824.4 ft from the starting point. To find the angle of rotation:
∠ = (824.4 / 1030.52) * 360 = 288.0 degrees.

Therefore, after 12 minutes, the car is located 824.4 ft from the starting point, and the angle of rotation is 288.0 degrees.