1. The problem statement, all variables and given/known data A ball is dropped from rest from the top of a 6.10m building, falls straight down, collides inelastically with the ground and bounces back. The ball loses 10% of it's K.E every time it hits the ground. How many bounces can happen and the ball still reach a height of 2.44m above the ground. 2. Relevant equations mgh = 1/2 mv2 xn = arn-1 (finding a term in a geometric series) 3. The attempt at a solution I can come to an answer easily enough using the two equations stated above and the ideas of gravitational P.E being converted to K.E (so mass cancels out) and constructing a geometric series that uses r = 0.9 to accommodate the energy loss. I have to essentially just guess terms until i'm in the right region and then increase or decrease my term until I reach the right answer. This seems somewhat messy to me, using trial and error. Is there a cleaner method, that will use the information of the final height I need it to reach? I'm just curious, thanks!