i am having difficulties figuring this out....
a ball has dropped from a height of 15m and bounces 60% of the previous height. the total distance ball travels after the 9th bounce is...
i got this equation done but i do not know how to calculate this to find the answer
15(0.6^9-1)/0.6-1
could you show me how to do it?
the trick here is that the first bounce has a different pattern than the following bounces
distance of 1st bounce = 15 ,...... just down
distance of 2nd bounce = 2(15)(.6) , ..... up and down
distance of 3rd bounce = 2(15)(.6^2)
distance of 4th bounce = 2(15(.6^3)
...
distance of 9th bounce = 2(15)(.6^8)
so total distance
= 15 + 8 terms
= 15 + 2(15)(.6) [ (.6^8 - 1)/(.6 - 1)]
I get 59.24
check my arithmetic
Sure! I can help you with that.
To determine the total distance the ball travels after the 9th bounce, we need to calculate the sum of the heights of all bounces.
The formula you provided is close, but there are some adjustments needed to calculate it correctly. Here's the corrected formula:
distance = 15 * ((1 - 0.6^10) / (1 - 0.6))
Let's break it down step by step:
Step 1: Find the ratio of the height of each bounce to the previous bounce. In this case, the ball bounces 60% of the previous height, so the ratio is 0.6.
Step 2: Calculate the total distance the ball travels after 10 bounces (including the initial drop). To do this, we can use the geometric series formula:
distance = initial height * ((1 - ratio^(n+1)) / (1 - ratio))
where n is the number of bounces. Since we want to calculate after the 9th bounce, we substitute n = 9:
distance = 15 * ((1 - 0.6^10) / (1 - 0.6))
Step 3: Solve the equation:
distance = 15 * ((1 - 0.6^10) / (1 - 0.6))
= 15 * ((1 - 0.6^10) / 0.4)
Now we can calculate the value using a calculator:
distance ≈ 15 * ((1 - 0.00604661) / 0.4)
= 15 * (0.99395339 / 0.4)
≈ 37.3517 meters
Therefore, the total distance the ball travels after the 9th bounce is approximately 37.3517 meters.