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A projectile is fired with speed v(0) at...

A projectile is fired with speed `v_(0)` at `t=0` on a planet named ' Increasing Gravity ' . This planet is strange one, in the sense that the acceleration due to gravity increases linearly with time `t` as` g(t)=bt`, where `b` is a positive constant. 'Increase Gravity'
At what angle with horizontal should the projectivle be fired so that it travels the maximum horizontal distance `:`

A

`theta=tan^(-1) (1)/(2)`

B

`theta=tan^(-1) (1)/(sqrt(2))`

C

`theta=tan^(-1)sqrt(2)`

D

`theta=tan^(-1)2`

Text Solution

Verified by Experts

The correct Answer is:
B
`R=v_(0)cos thetaxxsqrt((6v_(0)sin theta )/(b))`
`:. (dR)/(d theta)=0 ` at `tan theta=(1)/(sqrt(2))`
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