A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring \frac{128}{145} feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 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 this means that the positive direction for y is down.) y= Take as the gravitational acceleration 32 feet per second per second.
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Step 1: We can use the equation of motion for an object under constant acceleration: y = y0 + v0t + (1/2)at^2 where y0 is the initial position, v0 is the initial velocity, a is the acceleration, t is the time, and y is the final position. Show more…
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