A ball is dropped from 1.5m and bounces back up 1.2m. How many times will the ball bounce before it loses 90% of its energy? I figued since the ball bouced .8 times the original hight and 10% of 1.5m is .15m that that when the bounce hight reached.15m that 90% of the energy (hight *gravity) was lost. Istarted with 1.5m times .8, then the result * .8 , and so on. 10 times results in a bounce hight of .16. Is this a correct approach?
.8^n = .1
n ln .8 = ln .1
n = 10.31
Your approach is close, but there is a slight error in your calculations. Let's go through it step by step to determine the correct number of bounces before the ball loses 90% of its energy.
First, we need to calculate the initial bounce height. Since the ball is dropped from a height of 1.5m and bounces back up to 1.2m, the initial bounce height is equal to the total distance traveled by the ball, which is 1.5m + 1.2m = 2.7m.
Next, we need to determine how much energy is lost with each bounce. If the initial bounce height is 2.7m, then 90% of this height represents the point at which 90% of the energy is lost. So, 90% of 2.7m is 0.9 * 2.7m = 2.43m.
Now, let's calculate the bounce height after each successive bounce using your approach of multiplying the previous bounce height by 0.8:
1st bounce: 2.7m * 0.8 = 2.16m
2nd bounce: 2.16m * 0.8 = 1.728m
3rd bounce: 1.728m * 0.8 = 1.3824m
4th bounce: 1.3824m * 0.8 = 1.10592m
5th bounce: 1.10592m * 0.8 = 0.884736m
6th bounce: 0.884736m * 0.8 = 0.707789m
7th bounce: 0.707789m * 0.8 = 0.566231m
8th bounce: 0.566231m * 0.8 = 0.452985m
9th bounce: 0.452985m * 0.8 = 0.362388m
10th bounce: 0.362388m * 0.8 = 0.28991m
After 10 bounces, the bounce height reaches approximately 0.29m, which is less than the 0.15m threshold you calculated earlier. Therefore, the correct answer is that the ball will bounce 10 times before it loses 90% of its energy.
Note: In each calculation, it's important to use the height after the previous bounce, not the initial height.