a. To calculate the maximum speed of a cabin on the Santa Monica Ferris wheel, we need to first determine the circumference of the wheel. The formula for the circumference is C = πd, where d is the diameter of the wheel.
C = π x 26m = 81.68m
The maximum speed occurs at the bottom of the wheel, where the distance traveled in one rotation is equal to the circumference of the wheel. The formula for speed is v = d/t, where t is the time taken for one rotation.
v = 81.68m/26s = 3.14m/s
Therefore, the maximum speed of a cabin on the Santa Monica Ferris wheel is approximately 3.14 m/s.
b. If the High Roller Ferris wheel had the same rotation period of 26 s, we can use the same formula as above to calculate the speed of a cabin.
C = π x 158.5m = 498.87m
v = 498.87m/26s = 19.19m/s
Therefore, if the High Roller Ferris wheel had the same rotation period of 26 s, the speed of a cabin would be approximately 19.19 m/s.
c. The actual maximum speed of the High Roller is given as 48 km/h. To determine the minimum period, we need to first convert the speed to meters per second.
48 km/h = 13.33 m/s
We can then use the formula v = d/t to solve for the minimum period.
t = d/v
C = π x 158.5m = 498.87m
t = 498.87m/13.33m/s = 37.41s
Therefore, the minimum period for the High Roller Ferris wheel is approximately 37.41 s.