A particle is projected upward through a medium with quadratic resistance. The terminal falling speed in that medium is V and the measured maximum height is H. The launch speed is:
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Question

A particle is projected upward through a medium with quadratic resistance. The terminal falling speed in that medium is V and the measured maximum height is H. The launch speed is:

G1 Physics · Accepted Answer

For upward motion with quadratic drag, H = (V²/2g)ln[1+(u/V)²]. Therefore 2gH/V² = ln[1+(u/V)²]. Exponentiating, exp(2gH/V²) = 1+(u/V)². Hence u = V√[exp(2gH/V²)−1]. Therefore option A is correct.