Consider a rubber ball freely falling from a height ` h = 4.9 m` onto a horizontally elastic plate. Assume that the duration of collision is negligible and the collisions with the plate is totally elastic .
Then the velocity as a function of time and the height as a function of time will be :

Options

A.
B.
C.
D.

Answer

B

Explanation

Consider downward direction negative and upward positive.
for downward motion, `v = - g t`.
For upward motion, `v = + g t`.
As the collisions are elastic, the magnitude of velocity will remain the same. The direction will change after each collision, starting with negative direction. Also, `v prop t`, hence the graph will be straight line.
Also, `h = 4.9 - (1)/(2) g t^(2)` (before collision)
`h = (1)/(2) g t^(2)` (after collision)
As `h prop t^(2)`, hence graph will be parabolic with `h = 4.9 m` at `t = 0`.