2025 MSHS PRELIMS P1 Q2
2025 MSHS PRELIMS P1 Q2
Secondary 4
6 marks
A stone is thrown vertically upwards such that its height, \(h\) metres from the ground at time \(t\) seconds after being thrown is given by the formula \(h=-9t^2+12t+1\).
- Explain the meaning of the constant term in the formula.[1]
- Express \(h\) in the form \(a(t+b)^2+c\), where \(a\), \(b\) and \(c\) are constants to be determined.[3]
- Hence state the maximum height attained by the stone and the time at which this occurs.[2]
Solution:
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Answer:(a) The initial height is \(1\text{ m}\) above the ground. (b) \(h=-9\left(t-\frac{2}{3}\right)^2+5\). (c) The maximum height is \(5\text{ m}\), occurring at \(t=\frac{2}{3}\text{ s}\).
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