A particle falling vertically from a height hits a plane surface inclined to horizontal at an ange ` theta` with speed ` v_0` and rebounds elastically (Fig. 2 (RP). 28). Find the distance aling the plane where it will hit second time.
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Explanation

Refer Fig. 2(EP) 29 . Taking moton of particle from (O) to (A) along ` Y- axis (i.e., ?_|_r to plane (OA) upwards), we have ` y= 0 , y=0 u_y = v_0 cos theta , a_y =- g cos theta, t= T`
As, ` y=y _0 + u_y t + 1/2 a_y t^2`, we have ` 0 =0 + v_0 cos theta T + ` 1/2 ( - g cos theta ) T^2`
On soling , ` T = ( 2 v _0 cos theta )/( g cos theta) = (2 v_0)/g`
Taking moton of particle along X-axis (i.e. , along the plane from (O) to (A) , we hae
` x =x_0 0,x = R , u _x = v_0 sin theta, ` a_x = g sin , ` t= T = ( 2 v_0)/g`
As, ` x= x_0 + u _x t + 1/2 a_x t^2`
` :. R= 0 + v_0 sin xx (2 v_0)/g + 1/2 ( g sin theta) xx ((2 v _0)/g) ^2 = (2 v_0^2 )/g sin + 1/2 g sin theta xx (4 v_0^2)/g^2` ltbr. ` = (2 v_0^2 [ sin hteta + sin theta ] = (4 v_0^2 )/g sin theta` .