A ball is dropped from a height of 10m if it rebounds approximately half the distance after each fall use a geometric series to approximate the total distance the ball travels before coming to rest?

Answer 1

The answer is 30m. Lets assume that the ball is dropped from a height of h. The ball will come down and go up, so in the first bounce it covers h+h/2 distance. The second bounce, it is h/2+h/4, the third it will be h/4+h/8 and so on.

The total distance covered would thus be h+h/2+h/2+h/4+h/4+h/8+h/8+........... =

h+h+h/2+h/4+h/8+........... (summing up adjacent values in pairs) = 2h+h*(1/2+1/4+1/8+.............) = 3h (by the geometric series formula, 1/2+1/4+1/8+.....=1)

Hence taking, h=10m in this case, the answer would be 10*3= 30m