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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'.
If angle of projection with horizontal is `theta` then the time of flight is `:`

A

`sqrt((6v_(0)sin theta)/(b))`

B

`sqrt((2v_(0)sin theta)/(b))`

C

`sqrt((3v_(0)sin theta)/(b))`

D

`sqrt((2v_(0))/(b))`

Text Solution

Verified by Experts

The correct Answer is:
A
`(dV_(y))/(dt)=-bt`
or `v_(y)=-(bt^(2))/(2)+v_(0)sin theta .....(1)`
`(dy)/(dt)=-(bt^(2))/(2)+v_(0)sin theta`
or `y=-(bt^(2))/(6)+v_(0)sin theta t ....(2)`
Putting `y=0` in equation `(2)`
`T=sqrt((6v_(0)sin theta )/(b))=` Time of flight .
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