Help me with this, please...
A ball is dropped vertically from a height of 80 meters. After each bounce, the ball reaches a maximum height equal to 60 percent of maximum height of the previous bounce.
a. Write the first three terms of the sequence. Explain how you know what they are.
b. Find the height to the nearest tenth of a meter of the ball after the eighth bounce. Show and
explain your work.
nvm, i think i found this one out :)
h=1+13t-5t²
A golf ball has a rebound percentage of 60%. If it is dropped from 30 feet, how high will it bounce on the 5th bounce?
a. To find the first three terms of the sequence, we need to understand the pattern of the ball's bounce. We know that after each bounce, the ball reaches a maximum height equal to 60 percent (0.6) of the maximum height of the previous bounce.
Let's start with the initial drop from a height of 80 meters, which we can consider as the first bounce. The maximum height reached after this bounce is 80 meters.
For the second bounce, the maximum height reached will be 0.6 times the previous maximum height. So, for the second bounce, the maximum height will be 0.6 multiplied by 80, which is 48 meters.
For the third bounce, the maximum height reached will be 0.6 times the previous maximum height. So, for the third bounce, the maximum height will be 0.6 multiplied by 48, which is 28.8 meters.
Therefore, the first three terms of the sequence are:
Term 1: 80 meters
Term 2: 48 meters
Term 3: 28.8 meters
b. To find the height of the ball after the eighth bounce, we can use the same pattern of multiplying the previous maximum height by 0.6 for each bounce.
We already have the first three terms of the sequence, so we can continue using the same pattern to find the height after the eighth bounce.
Term 4: 0.6 times 28.8 meters = 17.28 meters
Term 5: 0.6 times 17.28 meters = 10.368 meters
Term 6: 0.6 times 10.368 meters = 6.2208 meters
Term 7: 0.6 times 6.2208 meters = 3.73248 meters
Term 8: 0.6 times 3.73248 meters = 2.239488 meters
Therefore, the height of the ball after the eighth bounce is approximately 2.2 meters (rounded to the nearest tenth of a meter).
Explanation of work:
For each bounce, we multiply the previous maximum height by 0.6 since it is given in the problem statement. This gives us the height of the ball after each bounce. We continue this multiplication process until we reach the desired bounce, in this case, the eighth bounce.