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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)^(2)tantheta)/(g),-(2v_(0)^(2)tan^(2)theta)/(g))`

B

`((2v_(0)^(2))/(g),-(2v_(0)^(2)tan^(2)theta)/(g))`

C

`((2v_(0)^(2)tan theta)/(g),-(2v_(0)^(2))/(g))`

D

`((2v_(0)^(2)tan^(2)theta)/(g),-(2v_(0)^(2)tan theta)/(g))`

Text Solution

Verified by Experts

The correct Answer is:
A
`(AB)/(BC) = ((1)/(2)g t^(2))/(v_(0)t) = tan theta`

`:. t = (2v_(0)tan theta)/(g)`
Now, x-coordinate `= v_(0)t = (2v_(0)^(2)tan theta)/(g)`
and y-coordinate `= - (1)/(2) g t^(2) =- (2v_(0)^(2)tan^(2) theta)/(g)`
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