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(B) Before the collision,the ball falls under gravity. Its velocity $v$ at time $t$ is given by $v = gt$. The kinetic energy $K$ is given by $K = \fra

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(B) Before the collision,the ball falls under gravity. Its velocity $v$ at time $t$ is given by $v = gt$. The kinetic energy $K$ is given by $K = \frac{1}{2} mv^2 = \frac{1}{2} m(gt)^2 = \frac{1}{2} mg^2 t^2$. Since $K \propto t^2$,the graph of $K$ versus $t$ is parabolic,opening upwards.During the collision,the ball is compressed. As the compression increases,the kinetic energy is converted into elastic potential energy. At the maximum compression,the velocity of the ball becomes zero,so the kinetic energy becomes zero. After reaching maximum compression,the ball starts to expand,and the elastic potential energy is converted back into kinetic energy until the ball leaves the surface.Thus,the kinetic energy decreases to zero during the compression phase and increases back to its original value during the expansion phase. This behavior is represented by a parabolic increase followed by a sharp dip to zero and a subsequent parabolic increase. Among the given options,graph $B$ represents this variation most appropriately.

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