A ball is thrown upward with an initial velocity V 0 from the surface of the earth. The motion of the ball is affected by a drag force equal to m γ v 2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is:

Question

A ball is thrown upward with an initial velocity V 0 from the surface of the earth. The motion of the ball is affected by a drag force equal to m γ v 2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is:, 1 γ g ln ⁡ 1 + γ g V 0, 1 γ g tan - 1 ⁡ γ g V 0, 1 γ g sin - 1 ⁡ γ g V 0, 1 2 γ g tan - 1 ⁡ 2 γ g V 0

MARKS App · Accepted Answer

Net force on ball, F = - m g - m γ v 2 a = - g - γ v 2 d v d t = - g - γ v 2 ∫ v = V 0 v = 0 d v g + γ v 2 = ∫ t = 0 t - d t 1 g γ t a n - 1 γ g v v = V 0 v = 0 = - t ∴ t = 1 γ g t a n - 1 γ g V 0

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