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202301160933 Exercise 3.4.B (Q29)

A ball is thrown vertically upward from the ground. Its displacement at time t is given by 20t-5t^2. Find the maximum distance of the ball from the ground and the time this occurs.

Extracted from Y. F. So & M. S. Wong. (1988). New Way Additional Mathematics.

Roughwork.

By differentiation wrt time

\begin{aligned} s(t) & = 20t-5t^2 \\ v(t) & = 20 - 10t \\ a(t) & = -10 \\ \end{aligned}

Its velocity is zero at some time t', i.e.,

\begin{aligned} 0=v(t') & =20-10t' \\ t' & = 2\,\mathrm{s} \\ \end{aligned}

once it reaches the maximum height

\begin{aligned} s(t') & = 20(2)-5(2)^2 \\ & = 20\,\mathrm{m} \\ \end{aligned}

This problem is not to be attempted.