SOLUTION: A special rubber ball is dropped from the top of a building 81m high. If after falling it bounces back to two-thirds of the previous bouncing height, then how high will it bounce

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A special rubber ball is dropped from the top of a building 81m high. If after falling it bounces back to two-thirds of the previous bouncing height, then how high will it bounce       Log On


   

Question 1084223: A special rubber ball is dropped from the top of a building 81m high. If after falling it bounces back to two-thirds of the previous bouncing height, then
how high will it bounce the 5th time?What is the total distance it has covered the 6th time it touches the ground? Solve using Geometric Sequence
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
a*r^(n-1) is height, with a=81, r=2/3 and n the number of times.
81*(2/3)^4=81*16/81=16 feet on the fifth time.
81 foot drop and hits 1 (81 feet)
bounces back up 54 feet (2/3 of 81)
drops 54 feet (189 feet distance) hits 2
rises 36 feet (225 feet distance) and falls 36 feet to hit 3 (261 feet distance)
rises 24 feet and falls 24 feet to hit 4 (309 feet distance)
rises 16 feet and falls 16 feet to hit 5 (341 feet)
rises 10 2/3 feet and falls 10 2/3 feet to hit 6 (362 1/3 feet).