System is shown in the figure. Velocity of sphere A is 9 `(m)/(s)`. Find the speed of sphere B.

Options

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)`

Answer

A

Explanation

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`