If you fire a paper clip straight up into the air with a rubber band, its height (in feet) above your hand time t seconds is given by: h = 64t - 16t^2.

Question

1) How long does it take the paper clip to reach its maximum height?

2) If your hand is 6 feet above the ground at "launch", what is the maximum height the paper clip attains?

3) At what 2 times is the paper clip traveling at a speed of 24 ft/sec?

4) What was the initial velocity imparted to the paper clip by the rubber band?

Answer 1

#1 as with any parabola, vertex is at t = -b/2a

#2 use the t from #1 and evaluate h(t)+6

#3 dh/dt = 64-32t
when is that 24 or -24?

#4 h(t) = vt-g/2 t^2