precalc
posted by ikora .
A ferris wheel is 28 meters in diameter and makes one revolution every 10 minutes. For how many minutes of any revolution will your seat be above 21 meters?

precalc 
Reiny
fit your data into a sine curve
period of sine curve = 10 minutes
2π/k = 10
k = 2π/10 = π/5
so start with
y = 14 sin π/5 t + 14
testing:
t = 0: y = 14sin0 + 14 = 14
t = 2.5 , y = 28
t = 5 , y = 14
t = 7.5 , y = 0
t = 10 , y = 14 , looks good
solve for
14 sin πt/5 + 14 = 21
sin πt/5 = 1/2
πt/5 = π/6 or πt/5 = 5π/6
t = 5/6 or t = 25/6 minutes
so time over 21 metres = 25/6  5/6 = 20/6 minutes
or 2 minutes and 20 seconds or 200 seconds 
precalc 
Steve
I'm sure the answer is unchanged, but I'd have set up the equation as
y = 14(1  cos pi/5 t)
That way, y(0) = 0, when the person gets on the wheel, rising to y(5) = 28 when it's 5 minutes later, at the top. And so on.
Respond to this Question
Similar Questions

math
A ferris wheel is 35 meters in diameter,and can be boarded at ground level. The wheel turns in a counterclokcwise direction, completing one full revolution every 5 minutes. Suppose that a t=0 you are in the three o'clock position. … 
Math
A ferris wheel is 30 meters in diameter and boarded in the six o'clock position from a platform that is 10 meters above the ground. The wheel completes one full revolution every 10 minutes. At the initial time t=0 you are in the twelve … 
Trig
A Ferris wheel is 40 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. … 
precalculus
A ferris wheel is 20 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. … 
PreCal
A Ferris wheel is 40 meters in diameter and boarded from a platform that is 5 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes one full revolution every 7 … 
PreCal
A Ferris wheel is 50 meters in diameter and boarded from a platform that is 5 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes one full revolution every 9 … 
precal
A Ferris wheel is 32 meters in diameter and makes one revolution every 4 minutes. For how many minutes of any revolution will your seat be above 24 meters? 
precalculus
A Ferris wheel is 10 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. … 
n
A ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. … 
mathprecalculus
A Ferris wheel is 50 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. …