Advanced MathHardSum of the times a projectile is at a given height
Advanced Math practice question
The height, in metres, of a ball t seconds after it is thrown is given by h(t) = 40t − 5t². The ball is at a height of 60 metres at two different times. What is the sum of those two times, in seconds?
Answer: 8
40t − 5t² = 60 → 5t² − 40t + 60 = 0 → t² − 8t + 12 = 0 → (t − 2)(t − 6) = 0. The times are 2 and 6 seconds; their sum is 8.
Common wrong answers
- If you answered 4
- 4 is the time of the maximum height, halfway between the two times.
- If you answered 6
- 6 is the later of the two times.
- If you answered 12
- 12 is the product of the two times.
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