Question

A ball bounces back to half of its previous height each time. If it is dropped from 256 meters, what is the height after the 6th bounce?

• A. 16 m
• B. 8 m
• C. 4 m
• D. 2 m

Hint:

For repeated halving, multiply by $(1/2)^n$ where $n$ is the number of reductions.

Answer 1

The Correct Option is C

To solve this problem, we need to determine the height reached by the ball after the 6th bounce. The ball bounces back to half of its previous height each time it hits the ground.

1. Initially, the ball is dropped from a height of 256 meters.
2. After the first bounce, the ball reaches half of 256 meters. Therefore, the height reached after the first bounce is \(\frac{256}{2} = 128\) meters.
3. After the second bounce, the ball reaches half of 128 meters. Therefore, the height after the second bounce is \(\frac{128}{2} = 64\) meters.
4. Continuing this pattern, the height after each subsequent bounce is calculated as follows:
   • Third bounce: \(\frac{64}{2} = 32\) meters.
   • Fourth bounce: \(\frac{32}{2} = 16\) meters.
   • Fifth bounce: \(\frac{16}{2} = 8\) meters.
   • Sixth bounce: \(\frac{8}{2} = 4\) meters.
5. Therefore, after the 6th bounce, the height the ball reaches is 4 meters.

Thus, the correct answer is:

4 m

This matches the correct option provided in the question: 4 m.