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# A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is $a(t) = 60t$, at which time the fuel is exhausted and it becomes a freely "falling" body. Fourteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to $-18\;ft/s$ in 5 seconds. The rocket then "floats" to the ground at that rate.(a) Determine the position function $s$ and the velocity function $v$ (for all times $t$). Sketch the graphs of $s$ and $v$.(b) At what time does the rocket reach its maximum height, and what is that height?(c) At what times does the rocket land?

## (a) $t \approx 45.5$ seconds(B) $$\begin{array}{l}{t=11.44 \sec } \\ {s(t)=1409.06 f t}\end{array}$$(c) $\mathrm{t}=45.6 \mathrm{s}$

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