A ferris wheel has radius of 25 m and its centre is 27 m above the ground. It rotates once every 40 seconds. Sandy gets on the ferris wheel at its lowest point and the wheel starts to rotate. at what time is she 35m above the ground
To find out when Sandy is 35m above the ground, we first need to determine the equation of the height of the ferris wheel as a function of time.
The height of Sandy above the ground at any given time can be determined by the equation:
h(t) = r + R*sin(2πt/T)
Where:
h(t) = height above the ground at time t
r = height of the centre of the ferris wheel above the ground
R = radius of the ferris wheel
T = time taken for one complete rotation of the ferris wheel
Given that r = 27m, R = 25m, and T = 40s, the equation becomes:
h(t) = 27 + 25*sin(2πt/40)
Now, to find out when Sandy is 35m above the ground, we need to solve the equation:
35 = 27 + 25*sin(2πt/40)
8 = 25*sin(2πt/40)
sin(2πt/40) = 8/25
2πt/40 = sin^(-1)(8/25)
2πt/40 = 0.318
t = 0.318 * 40 / (2π)
t ≈ 8.1 seconds
Therefore, Sandy is 35m above the ground approximately 8.1 seconds after she boards the ferris wheel.