Algebra question

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^2 + 151t + 423h

Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? 

The rocket splashes down after ______ seconds. 

How high above sea-level does the rocket get at its peak? 

The rocket peaks at _______ meters above sea-level.

Answer 1

h(t) = -4.9t^2 +151t +423 = 0

use quadratic formula, t = 19.52 seconds

h'(t) = -9.8t +151 =0

t= 151/9.8 = 15.4 seconds for max h

max h = -4.9(15.4)^2 +151(15.4) +423 = (151-4.9(15.4))(15.4) +423

=151-75.5)(15.4) +423 = 75.5(15.4) +423 = 1163+423 = 1586 meters