Posted by **-** on Monday, November 16, 2009 at 7:54pm.

The height, h, in metres, above the ground of a rider on a Ferris wheel can be modelled by the equation:

h= 10 sin ((pi/15 t) - 7.5) + 12

where t is the time, in seconds.

At t=0, the rider is at the lowest point. Determine the first two times that the rider is 20 m above the ground, to the nearest hundredth of a second.

- Math -
**Reiny**, Monday, November 16, 2009 at 9:40pm
we want h to be 20

20 = 10 sin ((pi/15 t) - 7.5) + 12

8 = 10 sin ((pi/15 t) - 7.5)

.8 = sin ((pi/15 t) - 7.5)

(pi/15 t) - 7.5) = .927295 or (pi/15 t) - 7.5) = pi - .927295 = 2.214297

Case 1: (pi/15 t) - 7.5) = .927295

pi/15 t = 8.427295

t = 40.237

case 2: (pi/15 t) - 7.5) = 2.214297

t = 46.28235

But the period of your wheel is 2pi/(pi/15) = 30 seconds, so my answers are for the second rotation.

Let’s subtract 30 seconds, to get

times of 10.24 sec and 16.28 seconds

check: if t = 10.24

h = 10sin(15/pi*10.24 - 7.5) + 12

= 20.016 (pretty close)

My other answer also works.

## Answer this Question

## Related Questions

- MATH - A Ferris wheel completes one revolution every 90 s. The cars reach a ...
- Calculus - The height above the ground of a rider on a large Ferries wheel can ...
- math - A ferris wheel has radius of 25 m and its centre is 27 m above the ground...
- Trig - A ferris wheel has a 14 meter diameter and turns counterclockwise at 6 ...
- Math (please help!) - The largest Ferris Wheel in the world is the London Eye in...
- Physics - Fairgoers ride a Ferris wheel with a radius of 5.00 {\rm m} . The ...
- Math -Trig Please help! - At one time, Maple Leaf Village (which no longer ...
- Math - A ferris wheel has a diameter of 10 m and takes 24 sec to make one ...
- Math (Trig) - a ferris wheel has a radius of 10m and is one meter above the ...
- Pre Calculus 12 - The height h, in metres, above the ground of a car as a ferris...

More Related Questions