Final answer:
Calculating the time for a ball to come to rest after being dropped and bouncing multiple times requires considering energy conservation and the coefficient of restitution, typically approached through an iterative or infinite series method.
Step-by-step explanation:
To determine the time taken for a ball to come to rest after being dropped and undergoing multiple collisions, we need to consider the energy conservation and the coefficient of restitution of the collisions. However, in a practical scenario and without a specified number of bounces or the exact restitution coefficient, calculating the total time would require an iterative or theoretical infinite series approach, as the ball would undergo an infinite number of collisions as it comes to rest. Common high school physics problems usually deal with a single bounce or a specific number of bounces, and do not extend to the point at which the ball comes to rest.
To find the time for a single bounce, you could use the kinematic equation for the distance fallen (d = ½ g t^2) to solve for the time (t) it takes for the ball to fall a distance (h), and then use the bounce height to calculate subsequent fall times until the ball comes to rest.