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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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