SOLUTION: A ball is dropped from a height of 30 m above the ground. It falls vertically and bounces off the ground. After each bounce it rises vertically to 80% of the height from which it

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A ball is dropped from a height of 30 m above the ground. It falls vertically and bounces off the ground. After each bounce it rises vertically to 80% of the height from which it      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1088533: A ball is dropped from a height of 30 m above the ground. It falls vertically
and bounces off the ground. After each bounce it rises vertically to 80% of
the height from which it fell. Write an expression for the total distance travelled by the ball from the initial drop to the 𝑛th impact with the ground.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A ball is dropped from a height of 30 m above the ground. It falls vertically
and bounces off the ground. After each bounce it rises vertically to 80% of
the height from which it fell. Write an expression for the total distance traveled by the ball from the initial drop to the 𝑛th impact with the ground.
----
1st impact:: 30m
2nd impact:: 2*0.8*30m
3rd impact:: 2*0.8*30m + 0.8[2*0.8*30m] = 2*0.8*30m(1+0.8)
4th impact:: 2*0.8*30m(1+0.8)^2
-----
nth impact:: 2*0.8*30m(1+0.8)^(n-2)
--------
Cheers,
Stan H.
-------------