Hello! I am having difficulty with my homework . Here is the question:
A Ferris wheel has a maximum height of 11m, a radius of 5m (which allows a 1.0m clearance at the bottom) and rotates once every 40 sec. As the ride begins you are half way to the top of the wheel.
b) What is the lowest you go as the wheel turns?
1.0 meters, when you are at the bottom where there is a 1.0m clearance above the
ground.
Explain why this must be a positive number.
Because the wheel doesn't go below the ground level.
c) How high will you be after 2.5 minutes?
The wheel makes one rotation in 40 seconds. One rotation is 360°, so its
angular speed is or
2.5 minutes is 2.5×60 or 150 seconds. So in those 150 seconds, the wheel
has turned through 9°×150 = 1350°. So we divide by 360° and observe
the quotient and remainder.
3
360)1350
1080
270
That's 3 complete rotations and 270° more. So after those three complete
rotations, you are right where you started, halfway on the way up to the top.
270° is 3 times 90°. So since you started halfway on the way up to the top,
after those three rotations, the first 90° would put you at the top. Then the
second 90° would put you half way back down (exactly opposite from where you
started). Then the third 90° rotation would put you at the bottom, where the
wheel has a clearance of 1.0 meter, so you are 1.0 meter high after 2.5 minutes.
[All you needed to know was that you started halfway up, the wheel's angular
speed, the 1.0m clearance at the bottom, and the 2.5 minutes. The wheel's
maximum height and radius were not needed. Maybe they were needed for the "a"
part which you didn't post.]
Edwin