A pendulum bob is released from a height. Each time it swings, the greatest height it reaches is 45 of the greatest height it reached on the previous swing. On the 2nd swing, the bob reaches a greatest height of 0.96 m. Find the height from which the bob was released. Give your answer in metres.
Need a hint?
Two swings each multiply the height by 45, so the 2nd swing height is 45 × 45 of the starting height.
Worked answer
- After the 1st swing the height is 45 of the release height.
- After the 2nd swing the height is 45 of that, so 1625 of the release height.
- 1625 of the release height = 0.96 m.
- Release height = 0.96 ÷ 1625 = 0.96 × 2516 = 1.5 m.
Answer: 1.5 m
The mistake this question tests
Habit
Percentage of a new total
Pupils divide 0.96 by 45 once, which only undoes one swing. The height has been multiplied by 45 twice, so the factor must be squared.
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