The height a ball bounces is less than the height of the previous bounce due to friction. The heights of the bounces form a geometric sequence.

Question

The height a ball bounces is less than the height of the previous bounce due to friction. The heights of the bounces form a geometric sequence. Suppose a ball is dropped from one meter and rebounds 94​%

of the height of the previous bounce. What is the total distance traveled by the ball when it comes to​ rest?

Does the problem give you enough information to solve the​ problem?

How can you write the general term of the​ sequence?

What formula should you use to calculate the total​ distance?

Answer 1

This is a geometric sum question - you can answer the question using the geometric summation formula, which the infinite geometric sum formula

Sum = A1/(1-r)

where A1 is the initial number in the sequence

R is the factor that it decreases

For this problem:

so A1 = 1 m and r is 0.94 since it bounces to 94% of original height

The infinite sum would be then S = (1m)/(1-0.94) = 16.67 m

however since the ball bounces up and then comes down this doesn't present the whole picture

for examples

the first drop

1 meters down

bounces 0.94 m up

falls 0.94 m down

notice the 0.94 happened twice!

so every bounces after the 1 meter drop happens twice except again for the 1 meter drop

so the answer should be 16.67 + 16.67 - 1 = 32.33333 meters total