Meters per second equation

Question

An evil supervillian has launched a missle from his/her submarine. The missle's height, in meters above sea level, as a function of time, , in seconds, is given by Find the time it takes for the missle to reach it's maximum height. Round your answer to three decimal places. How many seconds? What is the maximum height? Round your answer to three decimal places. meters

Answer 1

h(t) = -4.9t^2 + 287t + 171

to find time of the max height take the derivative and set it equal to zero

h'(t) = -9.8t + 287 = 0

t= 287/9.8 = 29.2857 seconds

plug that value of t into the original equation to solve for maximum height:

max height = h(287/9.8) = -4.9(287/9.8)^2 + 287(287/9.8) + 171 = 4202.5 + 8405 + 171= 12,778.5 meters

12,778.5 meters in 29.286 seconds at maximum height