2015 · Q30
When a ball bounces, it rises to 2/3 of the height from which it fell. If the ball is dropped from a height of 36 m, how high will it rise at the third bounce?
Elementary MathematicsNumber System
- A101/3 m
- B102/3 m
- C121/3 m
- D122/3 m
Explanation
This is a geometric-progression rebound problem (the options print mixed fractions, e.g. 102/3 means 10 2/3). Each bounce reaches 2/3 of the previous height, so after n bounces the height is 36 × (2/3)ⁿ. For the third bounce: 36 × 8/27 = 288/27 = 32/3 = 10⅔ m, i.e. option (b). The trap is stopping at two bounces (16 m) or forgetting the initial 36 m factor. Hence option (b).