A ball is dropped from 400 ft what is the height of the ball on the 6th bounce?
1 bounce =280 ft
2 bounce= 196 ft
3 bounce = 137.2
How do I figure this out?
280/400 = 0.7
196/280 = 0.7
137.2/196 = 0.7
Looks like the height on the nth bounce is 400*0.7^n
To find the height of the ball on the 6th bounce, you need to calculate the total distance traveled by the ball after 6 bounces. Since each bounce follows a pattern, you can use the given information to determine the distance covered by each bounce.
Initially, the ball is dropped from a height of 400 ft. So, on the first bounce, the ball rises to a height of (400 - 280) ft, which is 120 ft.
On the second bounce, the ball rises to a height of (280 - 196) ft, which is 84 ft.
On the third bounce, the ball rises to a height of (196 - 137.2) ft, which is 58.8 ft.
Since the pattern is now established, you can calculate the height of the 4th, 5th, and 6th bounce as well.
On the fourth bounce, the ball rises by (137.2 - 96.96) ft, which is 40.24 ft.
On the fifth bounce, the ball rises by (96.96 - 67.872) ft, which is 29.088 ft.
On the sixth bounce, the ball rises by (67.872 - 47.1696) ft, which is 20.7024 ft.
Now, you can add up the heights to find the total height of the ball on the 6th bounce:
Height of 1st bounce + Height of 2nd bounce + Height of 3rd bounce + Height of 4th bounce + Height of 5th bounce + Height of 6th bounce
= (120 + 84 + 58.8 + 40.24 + 29.088 + 20.7024) ft
= 352.8304 ft
Therefore, the height of the ball on the 6th bounce is approximately 352.8304 ft.
To figure out the height of the ball on the 6th bounce, you can use the information given about the heights of each bounce.
First, let's establish a pattern. From the information provided, we can see that each subsequent bounce is a fraction of the previous bounce. Specifically, each bounce is 70% of the previous bounce.
To find the height of the ball on the 6th bounce, we need to apply this pattern. Start with the initial height of 400 ft and calculate each bounce height by multiplying the previous bounce height by 0.7.
Here's the calculation step-by-step:
1st bounce: 400 ft (given)
2nd bounce: 400 ft * 0.7 = 280 ft
3rd bounce: 280 ft * 0.7 = 196 ft
4th bounce: 196 ft * 0.7 = 137.2 ft
5th bounce: 137.2 ft * 0.7 = 96.04 ft
6th bounce: 96.04 ft * 0.7 = 67.228 ft
Therefore, the height of the ball on the 6th bounce is approximately 67.23 ft.
Note: The heights provided for each bounce (280 ft, 196 ft, 137.2 ft) are used to establish the pattern and calculate the subsequent bounces. However, they are not consistent with the actual physics of a bouncing ball as different factors (such as elasticity, friction, etc.) affect the height of the ball during each bounce.