16Hit1600
Advanced MathVery hardDuration above a height

Advanced Math practice question

A ball's height, in metres, t seconds after it is thrown is h(t) = −5t² + 20t. For how many seconds is the ball higher than 15 metres?

Answer: 2

h(t) = 15 when −5t² + 20t = 15, i.e. t² − 4t + 3 = (t − 1)(t − 3) = 0: t = 1 and t = 3. Between those times the ball is above 15 m, so for 3 − 1 = 2 seconds.

Common wrong answers

If you answered 1
1 is when the ball first reaches 15 m, not how long it stays above.
If you answered 3
3 is when it comes back down to 15 m.
If you answered 4
4 is the total flight time (h = 0 at t = 4), not the time above 15 m.

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