A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-fourths the height of the previous bounce. Find the total vertical distance travelled by the all in ten bounces.
The height of each number bounce (n) is shown as:
h(n) = 6(0.75)^n
We want to find h(10)
h(n) = 6(0.75)^n
Time Height
0 6
1 4.5
2 3.375
3 2.53125
4 1.8984375
5 1.423828125
6 1.067871094
7 0.8009033203
8 0.6006774902
9 0.4505081177
10 0.3378810883
Adding up each bounce from 1-10, we get:
16.98635674
Since vertical distance means both up and down, we multiply this number by 2 to get:
16.98635674 * 2 = 33.97271347
Then we add in the initial bounce of 6 to get:
33.97271347 + 6 = 39.97271347 feet
The height of each number bounce (n) is shown as:
h(n) = 6(0.75)^n
We want to find h(10)
h(n) = 6(0.75)^n
Time Height
0 6
1 4.5
2 3.375
3 2.53125
4 1.8984375
5 1.423828125
6 1.067871094
7 0.8009033203
8 0.6006774902
9 0.4505081177
10 0.3378810883
Adding up each bounce from 1-10, we get:
16.98635674
Since vertical distance means both up and down, we multiply this number by 2 to get:
16.98635674 * 2 = 33.97271347
Then we add in the initial bounce of 6 to get:
33.97271347 + 6 = 39.97271347 feet