Question

at the lincoln county fair, aniyah rides a ferris wheel with a radius of 16 feet that is rotating at a rate of two revolutions every minute. how fast is aniyah rising when she is going in the upward direction and her seat is 20 feet above ground level? if necessary, round result to one decimal place. aniyah is rising at the rate of:

Answer 1

Aniyah is rising at a rate of 512π^2 feet per minute when she is going in the upward direction and her seat is 20 feet above ground level.

Step-by-step explanation:

To find the rate at which Aniyah is rising when she is going in the upward direction on the ferris wheel, we can use the concept of centripetal acceleration. The formula for centripetal acceleration is a = rω^2, where a is the centripetal acceleration, r is the radius, and ω is the angular velocity.

In this case, the ferris wheel has a radius of 16 feet and is rotating at a rate of 2 revolutions per minute. We need to convert the revolutions per minute to angular velocity in radians per minute by multiplying by 2π. So, ω = 2(2π) = 4π radians per minute.

Now we can substitute the values into the formula to find the centripetal acceleration: a = (16 feet)(4π radians per minute)^2 = 256π^2 feet per minute^2.

Finally, to find the rate at which Aniyah is rising, we need to find the derivative of the height function. The derivative of h(t) = r + a(t) is dh/dt = da/dt = 2(256π^2) = 512π^2 feet per minute.

So, Aniyah is rising at a rate of 512π^2 feet per minute when she is going in the upward direction and her seat is 20 feet above ground level.