Homework SourseA ball has the property that each time if falls from a heigh
A ball has the property that each time if falls from a height h onto a level, rigid surface, it will rebound to a height rh, where r(0<r<1) is a number called the coefficient of restitution. A super ball with r=0.5 is dropped froma height of 20 meters. If the ball cont. to bounce indefinitely, find the total distance the ball travel.
Solution
first the ball falls h meters, then rebounds to rh and falls back distance rh, then again rebounds at height r^2h and falls back and so on So the distance travelled is h+2rh+2r^2h+2r^3h+... =h+2rh(1+r+r^2+...) =h+2rh *1/(1-r) =h+2rh/(1-r) =(h-rh+2rh)/(1-r) =(h+rh)/(1-r) =h*(1+r)/(1-r) when h=20 and r=.5 the distance is 20*1.5/.5=60 meters I used that (1+r+r^2+...)=1/(1-r) when r<1
