Ask Question
15 January, 21:20

A ball is dropped from a height of 10 meters. With each bounce, the height decreases by 15% (Be careful with your math here) What is the height of the ball after the 5th bounce? How many bounces must the ball take in order to be below 1 meter in height? How does this relate to a geometric sequence?

+3
Answers (1)
  1. 16 January, 00:06
    0
    This is an exponential decay.

    Initially, the maximum height is 10m.

    After the first bounce, the height decreases by 15%, then the new maximum height is:

    10m - 10m*0.15 = 10m*0.85

    After the second bounce, we have another 15% decrease, the new height is:

    10m*0.85 - 10m*0,85*0.15 = 10m*0.85^2

    You can see now that the equation that models this situation is:

    H (n) = 10m*0.85^n

    Where n is the number of times that the ball bounced.

    Then, if n = 5 we have that:

    H (5) = 10m*0.85^5 = 4.437m

    This does relate to a geometric sequence because this is an exponential (decreasing) relation.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A ball is dropped from a height of 10 meters. With each bounce, the height decreases by 15% (Be careful with your math here) What is the ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers