JEE Main · 2009 · 12 Apr 2009 · Offline · Kinematics

While the ball falls its speed grows uniformly as $v=gt$, and the perfectly elastic bounce reverses the velocity instantly without any loss, so the speed then falls back to zero on the way up and the pattern repeats; a graph of velocity against time is therefore a straight-line sawtooth that flips sign at each bounce. The height meanwhile follows $h=\frac{1}{2}g{t}^2$ downward and an identical parabola upward, so it traces a series of equal parabolic arcs returning to the same maximum each time. The correct choice is the pair showing this sawtooth velocity together with the repeating parabolic height.