The drag force coming from air resistance is proportional to the square of the v

Question

The drag force coming from air resistance is proportional to the square of the velocity with magnitude .

a) Since the air resistance increases rapidly with increasing speed, a baseball falling vertically will have its acceleration go to zero when its speed approaches a certain value called the

terminal speed. Find an expression for in terms of the drag coefficient b, gravitational acceleration g and the mass of the ball m.

You throw a baseball straight up in the air with initial speed equal to .

b) What is the balls acceleration when its speed is half its terminal speed and it is moving up? c) Repeat b) when the ball is moving down.

Explanation / Answer

Let the drag force R = kv^2 a) terminal velocity is reached when the gravitational force = R kv^2 = mg v= (mg/k)^0.5 b) moving up mg+R = ma ma = mg+(mg/k)*k/4 = mg+mg/4 a = 5g/4 = 12.25 m/sec^2 c) moving down ma = mg-R = mg - (mg/k)*k /4 = mg-mg/4 a = 3/4 g = 7.35m/sec^2

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