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
More 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...
- Math (Trig) - a ferris wheel has a radius of 10m and is one meter above the ...
- Math -Trig Please help! - At one time, Maple Leaf Village (which no longer ...
- Math - A Ferris wheel has a radius of 35m and starts at 2m above the ground. It ...
- Math (please help!) - The largest Ferris Wheel in the world is the London Eye in...
- trig question - A Ferris wheel has a deameter of 50m. The platform at the bottom...
- Advanced Functions - The vertical position, h, in metres, of a gondola on a ...
- Trig - A ferris wheel has a 14 meter diameter and turns counterclockwise at 6 ...