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 pi over 3 radians. How high from the ground is the white plank after this motion?

Answer 1

The white plank will be 2 feet high from the ground after the water wheel rolls forward through an angle of pi/3 radians.

Step-by-step explanation:

To find the height of the white plank after the motion, we need to calculate the vertical displacement of the plank. Since the radius of the water wheel is 4 feet and the bottom of the wheel is 1 foot from the ground, the initial height of the white plank is 5 feet. The angle through which the wheel rolls is pi/3 radians.

The vertical displacement of the plank can be calculated using the formula: displacement = radius * (1 - cos(angle))

Substituting the values, we get: displacement = 4 * (1 - cos(pi/3))

Simplifying further, displacement = 4 * (1 - 0.5) = 2 feet.

Therefore, the white plank will be 2 feet high from the ground after this rolling motion.

Answer 2

Answer:7 ft

Step-by-step explanation:

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