Question

A ball always bounces to 3/5 of the height from which it is dropped. The ball is dropped from 1.8m and bounces 3 times. How many times will it rise from the third bounce?

Answer 1

Answer: 2.92h

Step-by-step explanation:

Given:

the ball falls and rebounds to 3/5 of the height it is falling.

Height = 1.8m

to calculate the total distance traversed by the ball up to the third bounce

D = h(0) + (3/5) x h(0) + (3/4) h(0) + (3/4) x (3/4) h(0) + (3/5) x (3/5) h(0) the ball falls and rebounds to 3/4 of the height it is falling.

this distance = down + up +down +up +down only

otherwise it will do the after 3rd bounce travel.

D = h(0) { 1 + 2 x (3/5) + 2 x (9/25) }

= 2.92h(0)

Answer 2

0.3888 m or 38.88 cm

Step-by-step explanation:

I believe the question should be "how high will it rise from the third bounce?"

Initial height = 1.8m

If the ball only rises to 3/5 of the previous height after each bounce, the heights after the first three bounces are;

`h_0=1.8m\\h_1=(3)/(5)*1.8=1.08\ m\\h_2=(3)/(5)*1.08=0.648\ m\\h_3=(3)/(5)*0.648=0.3888\ m`

The ball will rise 0.3888 m or 38.88 cm from the third bounce