Question

A ball is thrown upward with an initial velocity Vo from the surface of the earth.The motion of the ball is affected by a drag force equal to mγv²(where m is mass of the ball , v is it's instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is :​

Answer 1

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Answer 2

Answer:

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Time taken by the ball to rise to its zenith is t = √1 / gY tan - 1 √ Y / g V0.

A ball is thrown upward with an initial velocity V₀ from the surface of the earth. The motion of the ball is affected by a drag force equal to mγν²

The net force ma on the body is,

ma = -mg  - mγν²

==> a = -(g + γν²) =

==> -gdt = dv/(1 + γν²/g) --(1)

integrating both sides t : 0 --> t and V: V0 --> 0,

x ~ 0 1 / 1 + x 2 dx = tan - 1 x

by substitution, and integrating (1),

-gt = - √ 9 / Y tan - 1 √ Y / g V0

==> t = 1 / gY tan - 1 √ Y / g V0 .

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