SOLUTION: Bouncing Ball A ball is dropped from a height of 9 ft. The
elasticity of the ball is such that it always bounces up one-
third the distance it has fallen.
(a) Find the total dis
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Question 1190153: Bouncing Ball A ball is dropped from a height of 9 ft. The
elasticity of the ball is such that it always bounces up one-
third the distance it has fallen.
(a) Find the total distance the ball has traveled at the instant
it hits the ground the fifth time.
(b) Find a formula for the total distance the ball has traveled
at the instant it hits the ground the nth time.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
hits ground once: 9 feet
bounces up 3 feet (12)
bounces down 3 feet (15)
bounces up 1 foot and back down 1 foot (17 feet) - has hit floor 3 times
bounces up 1/3 foot and back down 1/3 foot (17 2/3 ft)- 4 times
bounces up 1/9 foot and back down 1/9 foot (17 8/9) feet, the answer.
-
9+2*{3*(1/3)^0+3*(1/3)^1+3*(1/3)^2+3*(1/3)^3...}
the infinite sum is 9+2*3/(1-1/3)=18 feet.
The n th time is 9+ 2*9(1/3)*{{1-(1/3)^(n-1)/(1-(1/3)}, and when n=5, the answer is 17.89 or 17 (8/9).
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