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A man standing on a hill top projects a ...

A man standing on a hill top projects a stone horizontally with speed `v_0` as shown in figure. Taking the co-ordinate system as given in the figure. Find the co-ordinates of the point where the stone will hit the hill surface.

A

`((2v_0^2tantheta)/g,(-2v_0^2tan^2theta)/g)`

B

`((2v_0^2)/g,(2v_0^2tan^2theta)/g)`

C

`((2v_0^2tantheta)/g,(2v_0^2)/g)`

D

`((2v_0^2tantheta)/g,(2v_0^2tan^2theta)/g)`

Text Solution

Verified by Experts

The correct Answer is:
A

Let it strike the incline after time T at a distance R.
Then, `R cos theta=V_(0)T : -R sin theta=-1/2 gT^(2)`
`rArr R sin theta=g/2 (R^(2) cos^(2) theta)/(V_(0)^(2)), rArr R=(2V_(0)^(2))/(g) (tan theta)/(cos theta)`
`x=R cos theta, y=-R sin theta`
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