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?

2 Answers
Daniel L.
Jun 10, 2018

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=10h1=10 and the ratio r=0.8r=0.8. The ratio is less than 11, 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=h11−r

S=10/(1-0.8)=10/0.2=100/2=50S=101−0.8=100.2=1002=50

Ultrilliam
Jun 10, 2018

bb( = 90)=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)

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