Consider a rubber ball freely falling from a height h = 4.9 m on a horizontal elastic plate. Assume that the duration of collision is negligible and the collision 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

For downward motion `v = -gt`
The velocity of the rubber ball increases in downward direction and we get a straight line between `v and t` with a negative slope .
Also applying ` y - y_(0) = ut + 1/2 at^(2) `
we get ` y- h = -1/2 gt^(2) rArr y = h -1/2 gt^(2) `
The graph between `y and t` is a parabola with `y = h ` at `t= 0` . As time increases `y` decreases.
For upward motion .
The ball suffer elastic collision with the horizontal elastic plate therfore the direction of velocity is reversed and the magnitude remains the same . Here, ` v= u - gt` where `u` is the velocity just after collision . As `t` increases , `v` decreases . We get a straight line between `v and t` with negative slope .
Also ` y = ut - 1/2 gt^(2)`
All these characteristics are represented by graph `(b)`.