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 `mgammav^2` (where m is mass of the ball, v is its instantaeous velocity and `gamma` is a constant).Time taken by the ball to rise to its zenith is :

Options

A. `1/sqrt(lambda g) sm^(-1)(lambda/g V_(0))`
B. `1/sqrt(lambda g)tan^(-1) (sqrt(lambda/g V_(0)))`
C. `1/sqrt(2lambda g)tan^(-1)(sqrt((2lambda)/g V_(0)))`
D. `1/sqrt(lambda g)ln^(-1) (1+sqrt(lambda/g V_(0)))`

Answer

B

Explanation

`a=(dv)/(dt) =-(g+lambda.v^(2)) rArr int_(v_(0))^(0) (dv)/(g+lambdav^(2))= int_(0)^(t)dt rArr -1/lambda int_(v_(0))^(0) (dv)/(v^(2) + (sqrt(g//r))^(2))= int_(0)^(t)dt`
`t=sqrt(1/(glambda))tan^(-1)[sqrt(lambda/g)v_(0)]`