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
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=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#

Jun 10, 2018

#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)#