1. The problem statement, all variables and given/known data A ball, which is launched in the air with velocity V, has inelastic collisions with the floor: the kinetic energy after each collision is k times the kinetic energy before the collision, where k<1. Assume that the gravitational acceleration is constant: g [m/s^2]. I was asked to show that the time interval between the nth and the (n+1)th bounce is tn=(2V/g)*kn/2. This was pretty simple using conservation of energy and motion along straight-line equations. The second question asks me to find the total time T the bouncing ball takes to come to rest. This is where I am stuck. 2. Relevant equations Conservation of energy -> mgh=½mV2 after the nth bounce Kinetic Energyn = kn(½mV2) which is equal to ½m(vn)2. height the ball reaches after the nth bounce -> hn=knV2/(2g) Motion along straight-line equations -> v=at, x=x0+v0t+½at2 Time interval between the nth and the (nth+1)th bounce -> tn=(2V/g)*kn/2 3. The attempt at a solution I honestly did not know where to start but I started with the thought that if the ball stops bouncing it means that hn would be zero. I splitted the time interval equation in (V/g)*kn/2 + (V/g)*kn/2) = tn. With the height of the ball equation i subbed one part of the time interval equation which results in tn=(V/g)*kn/2 + √(2hn/g). I moved everything except the height part to the left and when removing the square root I got (tn)2 - (V2/g2)*kn = 2hn/g. It is clear that for hn to be zero then (tn)2 has to be equal to (V2/g2)*kn. I have a feeling I'm drifting towards a wrong answer with this because I really do not know what to do now. Did I approach this problem correctly? If so, what do I have to do to finalize it and if not, I would really appreciate some help to push me in the right direction!