NASA rocket launch

Question

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h (t) = -4.9t? + 37t + 374. For each of the answers below, put your numerical answer, rounded to 1 decimal place, in the first box and the units, spelled out completely, in the second box. How long does it take until the rocket reaches its maximum height? What is the maximum height reached by the rocket? Assuming that the rocket will splash down into the ocean, how long does it take for splashdown to occur?

Answer 1

v(t) = dh/dt = - 9.8t + 37 = 0, t = 37/9.8 s = 3.8 s

h_max = h(3.8) = 447.6 m

h(t) = - 4.9t² + 37t + 374 = 0; t = 13.3 s