Bouncing Ball A ball is dropped from a height of The elasticity of the ball is such that it always bounces up one third the distance it has fallen.
Find the total distance the boll has traveled at the instant it hits the ground the fifth time.
Find a formula for the total distance the ball has traveled at the instant it hits the ground the time.
The total distance traveled by the ball when it hits the ground for the fifth time.
The ball is fallen from a height of , the ball bounces up one third the distance it has fallen.
Approach: The partial sum of the geometric series is .
When the ball hits the ground for the first time, it has traveled a distance and the distance traveled up and down for the second time is , it will travel twice when up and down and similarly, it will be the one third of the previous distance for further bounces
Form a sequence-
The total distance for the fifth time can be written in the form-
Formula for the total distance for the time.
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