NIMCET 2008 — Reasoning PYQ
NIMCET | Reasoning | 2008From a height of 16 m, a ball fell down and each time it bounces half the distance back. What is the total distance travelled?
Preparing for Excellence...
From a height of 16 m, a ball fell down and each time it bounces half the distance back. What is the total distance travelled?
This problem can be solved using the concept of an Infinite Geometric Progression (GP).
1. Visualizing the Movement:
Initial Drop: The ball falls .
First Bounce: It goes up (half of ) and comes down . Total for this bounce: .
Second Bounce: It goes up (half of ) and comes down . Total for this bounce: .
This pattern continues infinitely.
2. Forming the Series:
The total distance can be written as:
3. Applying the Formula:
The terms inside the bracket form an infinite geometric series where:
First term
Common ratio (which is less than )
The sum of an infinite GP is given by:
Substituting the values:
4. Total Distance Calculation:
Now, add the initial drop to the sum of the bounces:
The total distance travelled by the ball is 48 m. Therefore, the correct option is (c).