Question

A ball is dropped from a height of 10 feet.Each time it hits the ground, it bounces to 80% of it's previous height. Find the total distance travelled by the ball?

Answer 1

See explanation.

Explanation:

Although the question is places in Physics, it can be answered using maths only.

The heights of the ball form a geometric sequence with `h_1=10` and the ratio `r=0.8`. The ratio is less than `1`, so the sequence is convergent (i.e. it has a finite sum). The sum of the sequence can be calculated as:

`S=h_1/(1-r)`

`S=10/(1-0.8)=10/0.2=100/2=50`

Answer 2

`bb( = 90)`

Explanation:

`d = 10 + color(red)(2) * 10 * 0.8 + color(red)(2) * 10 * 0.8^2 + ....`

`= 10(1 + 2 * 0.8 + 2 * 0.8^2 + ....)`

`= 10(2 + 2 * 0.8 + 2 * 0.8^2 + ....+ 2*0.8^(k-1) + ... ) - 10`

`= 10* 2/(1 - 0.8) - 10`

`bb( = 90)`