Irodov Problem 1.31
Let the point of contact of the ball with the inclined plane for the first time be the origin in our Cartesian coordinate system and let t=0. Then the position of the ball after reflection at any time is given by,
Here V0 is the velocity at first impact on the inclined plane.
This can be seen from the figure drawn beside.
Thus where ever the ball meets the plane, the inclined plane relation must also hold true. In other words,
Now knowing the time we can calculate the x coordinate of where the ball hits the inclined plane as,
Now the distance l traveled by the ball along the inclined plane is given as,
Since the ball fell a height h before hitting the inclined plane, it must have attained a velocity of