a rocket is launched and its height in meters is a function of time in seconds the function is described by the equation h=-5t↑2 +200t+30 determine the maximum height of the rocket and when it occurs

Answer 1

-5t^2 +200t + 30

take the derivative and set equal to zero

-10t +200 = 0

t =200/10 = 20 seconds to reach max height

-5(20)^2 + 200(20) + 30 = -2000+4000+30 = 2030 meters = max height

(minor note: this problem uses -5 where the actual effect of gravity, at sea level, would have -4.9)

Answer 2

Hello Jake,

Essentially, you're being asked to find the vertex of the parabola h = -5t² + 200t + 30

t = -b/2a where a = -5, b = 200 ---> t = -200/(2*-5) = -200/-10 = 20 -> The maximum height occurs at t = 20 s

Max height: Plug 20 in the rocket equation: h = -5(20)² + 200(20) + 30 = -5(400) + 4000 + 30 = 2030

Answer: the maximum height is 2030 meters and it occurs when t = 20 seconds.