An object launched vertically upward from the ground with a speed of 50 \mathrm{~m} / \mathrm{s} bounces off of the ground on the return trip with a coefficient of restitution given by C_{R}=0.9, meaning that immediately after a bounce the upward speed is 90 \% of the previous downward speed. The ball continues to bounce like this; what is the total amount of time between when the ball is launched and when it finally comes to a rest? Assume the collision time is zero; the bounce is instantaneous. Treat the problem as ideally classical and ignore any quantum effects that might happen for very small bounces.
Answer Choices
A. 71 \mathrm{~s}
B. 100 \mathrm{~s}
C. 141 \mathrm{~s}
D. 1000 \mathrm{~s}
E. \infty (the ball never comes to a rest)