A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 17 feet. The ball is started in motion from the equilibrium position with a downward velocity of 4 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second.

Question

Giovanna Crane

Physics

29 November, 11:58

A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 17 feet. The ball is started in motion from the equilibrium position with a downward velocity of 4 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second.

+4

Answers (2)

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Cristian Lyons · Answer 1

y = (0 - 4 * sqrt (6) / 48) * exp ((-16 - 4 * sqrt (6)) * t + (0 + 4 * sqrt (6) / 48) * exp ((-16 + 4 * sqrt (6)) * t)

Explanation:

Assume that the gravitational acceleration is 32 feet per second square. y = (0 - 4 * sqrt (6) / 48) * exp ((-16 - 4 * sqrt (6)) * t + (0 + 4 * sqrt (6) / 48) * exp ((-16 + 4 * sqrt (6)) * t)

Anderson Vaughn · Answer 2

Anderson Vaughn 29 November, 12:25

0

twelve because it is the answer