v1 Algebra, STD2 A4 2022 HSC 9 MC

An object is projected vertically into the air. Its height, \(h\) metres, above the ground after \(t\) seconds is given by \(h=-5 t^2+80 t\).

How far does the object travel in the first 10 seconds?

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\(C\)

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\(\text{By symmetry (or graph), object reaches max height at}\ \ t=8\ \text{seconds.}\)

\(\text{Find}\ h\ \text{when}\ \ t=8:\)

\(h=-5 \times 8^2-10 \times 8= 320 \)

\(\text{When}\ \ t=10\ \ \Rightarrow\ \ h=300\ \text{(from graph)}\)

\(\therefore\ \text{Total distance}\ = 320 + 20=340\ \text{metres}\)

\(\Rightarrow C\)