A ferris wheel has a radius of 25 metres and is 27 meters above the ground. the time it takes for a full rotation is 40 seconds. so what time is the person on the ferris wheel at at 35 m
To find out what time the person is at when the ferris wheel is at a height of 35 meters, we first need to calculate the period of the ferris wheel's rotation.
Since the ferris wheel takes 40 seconds for a full rotation, its period can be calculated by dividing the total time for one full rotation by 2 (since the motion is periodic):
Period = 40 seconds / 2 = 20 seconds
Next, we need to determine the angular frequency (omega) of the ferris wheel. The angular frequency is defined as the rate at which the ferris wheel completes one full rotation in time.
Angular frequency (omega) = 2 * π / Period
Angular frequency (omega) = 2 * π / 20 = π / 10
Now, we can find the time at which the person is at a height of 35 meters. The equation for the height of the person on the ferris wheel as a function of time is given by:
Height(t) = Amplitude * cos(omega * t) + Height_offset
Height(t) = 25 * cos(π/10 * t) + 27
To find the time when the person is at 35 meters, we set the equation equal to 35 and solve for t:
35 = 25 * cos(π/10 * t) + 27
8 = 25 * cos(π/10 * t)
0.32 = cos(π/10 * t)
To solve for t, we take the inverse cosine of 0.32:
π/10 * t = cos^(-1)(0.32)
π/10 * t ≈ 1.243
t ≈ 1.243 * 10 / π
t ≈ 3.96 seconds
Therefore, the person on the ferris wheel is at a height of 35 meters approximately 3.96 seconds after the start of the ride.