Year 11 Maths - Methods Quadratics

Quadratic Models

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Questions

Question 1

28627

The height \(h\) metres of a stone, \(t\) seconds after being thrown vertically upwards is given by \(h = 40t - 5{t^2}\). At what time is it first at 60 m?

Answer

\(t = 2\) seconds

Worked Solution

\begin{align}
&\begin{aligned}
h&=40 t-5 t^{2} \\
60&=40 t-5 t^{2}
\end{aligned}\\
&\begin{aligned}
5 t^{2}-40 t+60&=0 \\
5\left(t^{2}-8 t+12\right)&=0 \\
5(t-2)(t-6)&=0 \\
\end{aligned}\\
&\therefore t=2 \text { or } t=6\\
&\therefore t=2 \text { seconds } \\
\end{align}

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