A golfer hits a ball such that the height, $h$ metres, of the ball above the ground $t$seconds l

Question

A golfer hits a ball such that the height, $h$ metres, of the ball above the ground $t$seconds later is given by$h=0.2t\left( 40-t \right)$. By expressing the function in the form $h=a{{\left( t-m \right)}^{2}}+n$, where $a$, $m$ and $n$ are constants, explain whether the ball can reach a height of $100$ metres.[2] Find the range of values of $t$ for which the ball is at most $75$ metres above the ground.[4]

Accepted Answer

(a) Maximum height $80\text{ m}$; the ball cannot reach $100\text{ m}$ (b) $0\leq t\leq15$ or $25\leq t\leq40$

2023 AISS 3AM EOY Q4

2023 AISS 3AM EOY Q4

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