A ball is dropped from a height of eight meters. Each time it hits the ground, it rebounds three-quarters of the distance it has fallen.  In theory, how far will the ball travel before coming to rest?

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Kellie - This is a geometric series ... here is how to set up the problem: 8 + (2)(3/4)(8) + (2)(3/4)(3/4)(8) + ... infinite terms Or simplified: 8 + 16(0.75 + 0.75^2 +0.75^3 + ...) Think of it this way, the ball initially falls 8m, then bounces up 6m then drops down 6m, then goes up 4.5m then goes back down 4.5m and this cycle continues infinitely with each successive rebound equal to 0.75 times the prior height. Use your formula for infinite series: 8 + (16)(.75)/(1-.75) = 8 + 48 = 56m Hope this helps