Question

A child playing at the balcony of his multi-stored apartment drops a ball from a height of 350 m. each time the ball rebounds, it rises 4⁄5^th of the height it has fallen through. the total distance travelled by the ball before it comes to rest is

Answer 1

The total distance traveled by the ball is 1750 m

Explanation:

First distance traveled by the ball = 350m

second distance traveled by the ball = 350 x 4/5

Third distance traveled by the ball = 350 x 4/5 x 4/5

Fourth distance traveled by the ball = 350 x 4/5 x 4/5 x 4/5

and this motion continues until the ball comes to rest.

Hence total distance traveled by the ball ,

S =  350 + 350 x 4/5 + 350 x 4/5 x 4/5  + 350 x 4/5 x 4/5 x 4/5.............upto 0

we can see that this a geometric series having

a = first term = 350

r = common ratio = 4/5

we know that sum of a geometric series is given by :

S = $\frac{a}{1-r}$

=> S = 350/(1-4/5)

= 350 x 5 = 1750

Hence the total distance traveled by the ball is 1750 m

Answer 2

Answer:

Total distance covered by the ball is D= 350 + (2*4/5 *350) + (2*4/5*4/5*350)+.....

D=350(1+2 (4/5 + (4/5*4/5) + ......) )

(4/5 + (4/5*4/5) + ......) is an infinite GP where Sn=a/(1-r)

Here, a=4/5

r=4/5

So, D=350(1+2(4))

D=3150m