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(C) When the ball is thrown horizontally,its initial vertical velocity is $v_y = 0$. As it falls under gravity,its vertical velocity becomes negative

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(C) When the ball is thrown horizontally,its initial vertical velocity is $v_y = 0$. As it falls under gravity,its vertical velocity becomes negative (downward) and increases linearly with time according to $v_y = -gt$. When the ball hits the ground,it undergoes an inelastic collision. The velocity changes from a negative value to a positive value (upward) instantaneously. Since the coefficient of restitution $e After the bounce,the ball moves upward with a positive velocity that decreases linearly due to gravity until it reaches its peak,then becomes negative again. Because the acceleration due to gravity $g$ is constant and acts downwards,the slope of the $v_y$ vs $t$ graph is constant and negative $(-g)$ throughout the motion. Thus,the segments of the graph are parallel straight lines with a negative slope. Option $(c)$ correctly shows these features.

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