Question

a ball is dropped from a height of 10 meters. each time it bounces, it reaches 50 percent of its previous height. the total vertical distance the ball has traveled when it hits the ground the fifth time is

Answer 1

l = 10
L- the total vertical distance
L = l+(l/2+l/4+l/8+l/16)*2 = 2*l+7/8*l=20+8.75=28.75m

Answer 2

Distance covered by the ball = 28.75 meters

Explanation:

A ball is dropped from a height of 10 meters.

Each time it bounces 50% of the previous height.

Distance covered by the ball when dropped from a height before 1st bounce = 10 meters

Ball bounced back after 1st bounce and covered a 50% distance of 10 meters = 5 meters

Again this ball goes down and covers distance before 2nd bounce = 5 meters

Now third time the ball bounced back and came down, so distance covered = 2.5 + 2.5 = 5 meters

In 4th bounce ball bounced back and came down, so distance covered = 2×1.25 = 2.5 meters

Similarly in 5th bounce distance covered by the ball =
`(1.25)/(2)* 2=1.25` meters

Total distance covered = 10 + 10 + 5 + 2.5 + 1.25

= 28.75 meters

Therefore, distance covered by the ball will be 28.75 meters.