A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 18 m above ground level?
y = 13+13sin(πt)
solve for t when y=18
then get dy/dt = 13πcos(πt)
There are other sin/cos functions you can use, but they will all produce the same result.
To find the speed at which the rider is rising, we first need to determine the angular speed.
The Ferris wheel completes one revolution every 2 minutes, which means it completes 2π radians (a full circle) in that time. Therefore, the angular speed (ω) can be calculated using the formula:
ω = (2π radians) / (2 minutes)
Simplifying this, we get:
ω = π radians / minute
Now, let's find the linear speed of the rider. The linear speed (v) is related to the angular speed (ω) and the radius (r) by the formula:
v = ω * r
Plugging in the given radius of 13 m and the angular speed we calculated, we have:
v = (π radians / minute) * 13 m
Simplifying this, we find:
v = 13π m / minute
Thus, the rider is rising at a speed of 13π meters per minute when the rider is 18 meters above ground level.