A public swimming pool that holds 45,000 gallons of water is going to be drained for maintenance at a rate of 100 gallons per mi
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Answer:
Step-by-step explanation:
Suppose at t = 0 the person is 1m above the ground and going up
Knowing that the wheel completes 1 revolution every 20s and 1 revolution = 2π rad in angle, we can calculate the angular speed
2π / 20 = 0.1π rad/s
The height above ground would be the sum of the vertical distance from the ground to the bottom of the wheel and the vertical distance from the bottom of the wheel to the person, which is the wheel radius subtracted by the vertical distance of the person to the center of the wheel.
(1)
where is vertical distance from the ground to the bottom of the wheel,
is the vertical distance from the bottom of the wheel to the person, R = 10 is the wheel radius,
is the vertical distance of the person to the center of the wheel.
So solve for in term of t, we just need to find the cosine of angle θ it has swept after time t and multiply it with R
Note that is negative when angle θ gets between π/2 (90 degrees) and 3π/2 (270 degrees) but that is expected since it would mean adding the vertical distance to the wheel radius.
Therefore, if we plug this into equation (1) then