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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. 1 – tan g 1 γ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ γ 0 V g
2. ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ γ γ 0 1 – V g 2 tan g 2 1
3. ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ γ γ 0 1 – V g sin g 1
4. ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ γ + γ 0 V g 1 ln g 1

Correct answer: 1 – tan g 1 γ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ γ 0 V g

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