Problema Solution
A certain ball is dropped from a height of x feet. It always bounces up to 2/3x feet. Suppose the ball is dropped from 10 feet and I'd caught exactly when is touches the ground after the 30th bounce. What is the total distance traveled by the ball? Express your answer in exponential notation.
Answer provided by our tutors
Here we are dealing with geometric series with first term a1 = 10 feet and common ratio r = 2/3.
We need to find the sum of the the first 30 terms.
We are using the formula for sum of geometric series:
where a1 is the first term and r is the common ratio.
In our case we have:
S30 = a1*(1-r^30)/(1 - r)
S30 = 10*(1-(2/3)^30)/(1 - (2/3))
S30 = 30 ft
The total distance the ball travels is 30 feet.