Name: Sum of First n Odd Numbers
Uploaded: 2019-07-19
Duration: 3 min 35 s
Description: The odd numbers sequence also forms an A.P. whose common difference is 2. In this video, we will learn to find the formula for the sum of first n odd numbers...

Question

A ball is dropped from a vertical height of

20 m

. Following each bounce, it rebounds to a vertical height of

\frac{5}{6}

its previous height. Assuming that the ball continues to bounce indefinitely, show that the maximum distance it can travel is

220 m

.

Accepted Answer

Initial height $= 20 m$

Height gained in first rebound $220 m$

Height gained in going down $= 20 \times \frac{5}{6}$

Height gained in second rebound $= 20 \times {(\frac{5}{6})}^{2}$

Height gained in going down $= 20 \times {(\frac{5}{6})}^{2}$

$⋮$

So, get series as

$20 + (2 \times \frac{5}{6} \times 20) + (2 \times \frac{5}{6} \times \frac{5}{6} \times 20) + \dots$

$= 20 + 40 [(\frac{5}{6}) + {(\frac{5}{6})}^{2} + \dots]$

$= 20 + 40 [\frac{\frac{5}{6}}{1 - \frac{5}{6}}]$ [ $∵ (\frac{5}{6}) + {(\frac{5}{6})}^{2} + . . . .$ is an infinite G.P with $a = \frac{5}{6}, r = \frac{5}{6}, S_{\infty} = \frac{a}{1 - r}$ ].

$= 20 + 40 (\frac{5}{6 - 5})$

$= 20 + 200$

$= 220$

Hence, the maximum travelling is $220 m$ .

A ball is dropped from a vertical height of $20 m$ . Following each bounce, it rebounds to a vertical height of $\frac{5}{6}$ its previous height. Assuming that the ball continues to bounce indefinitely, show that the maximum distance it can travel is $220 m$ .

Important Questions on From Patterns to Generalizations: Sequences and Series

Learn and Prepare for any exam you want !

A ball is dropped from a vertical height of 20 m. Following each bounce, it rebounds to a vertical height of 56 its previous height. Assuming that the ball continues to bounce indefinitely, show that the maximum distance it can travel is 220 m.

Important Questions on From Patterns to Generalizations: Sequences and Series

Learn and Prepare for any exam you want !

A ball is dropped from a vertical height of $20 m$ . Following each bounce, it rebounds to a vertical height of $\frac{5}{6}$ its previous height. Assuming that the ball continues to bounce indefinitely, show that the maximum distance it can travel is $220 m$ .