Question

A water wheel has a radius of 4 feet and the bottom of the wheel is 1 foot from the ground. One plank is painted white and it starts at the top of the wheel. The wheel is rolled forward through an angle of StartFraction pi Over 3 EndFraction radians. How high from the ground is the white plank after this motion?

Answer 1

Explanation:

We can start by drawing a diagram of the situation:

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/ \

/ \

/ \

/ \

_______/_________\_______

4ft 4ft

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1ft h ft

We can see that the distance from the center of the wheel to the white plank is also 4 feet (since the radius of the wheel is 4 feet).

Next, we need to find the height of the white plank after the wheel is rolled forward through an angle of π/3 radians.

To do this, we can use trigonometry. Let's call the height of the white plank after the motion "h". We can use the sine function to relate the angle through which the wheel is rolled and the height of the plank:

sin(π/3) = h/4

Simplifying this equation, we get:

h = 4sin(π/3)

h = 4(√3/2)

h = 2√3

Therefore, the height of the white plank after the motion is 2√3 feet from the ground.