Maximum Height Reached After Two Successive Bounces

Problem Statement

Let the $y$y-axis point vertically upward, with the floor at $y = 0$y=0. At time $t$t, a small ball of mass $m$m is released from rest at height $y = H$y=H and falls freely. The ball hits the floor and bounces up, reaches its highest point, falls again, and makes a second collision with the floor.

Let the coefficient of restitution (bounce coefficient) between the floor and the ball be $e$e. Ignore air resistance and the size of the ball. Let the magnitude of gravitational acceleration be $g$g.

Find the height $h_2$h2​ reached by the ball after the second collision.

Constraints

• Initial height: $H = 100 \text{ m}$H=100 m
• Coefficient of restitution: $e = 0.5$e=0.5
• Magnitude of gravitational acceleration: $g = 9.8 \text{ m/s}^2$g=9.8 m/s2

Input Format

Find the value of $h_2$h2​ and give the answer as a positive integer equal to $h_2$h2​ multiplied by 100.