NASA launches a rocket at t = 0 seconds.

Question

NASA launches a rocket at  seconds. Its height, in meters above sea-level, as a function of time is given by .Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?

The rocket splashes down after _______   seconds.

The rocket peaks at  _______  meters above sea-level.

Answer 1

splashdown is when h(t) = 0 = -4.9t^2 + 184t + 423

t= 184/9.8 + (-1/9.8)sqr(184^2 +4(4.9)(423)) = 39.7 seconds

rocket peaks when the derivative = zero

-9.8t + 184=0

t = 184/9.8 = 18.8 seconds for peak, maximum height

splash down would have been exactly twice 18.8 or 37.6 seconds, if the rocket had started at ground level instead of 423 meters. It took about another 2 seconds to get down those 423 meters.