A model rocket is fired up in the air from an elevated launchpad. Its height, in metres, is given by the equation: h(t) = −5t2+80t+20.

Question

What is the maximum height of the rocket and how long does it take to achieve it? When, to the nearest tenth of a second, does the rocket hit the ground?

Answer 1

-10t +80 = 0

t = 10 seconds

plug 10 into the quadratic to get max height

-5(10)^2 + 80(10) + 20 =

-500 + 800 + 20 = 320 meters maximum

It hits the ground when -5t^2 +80t + 20 = 0

t^2- 16t = 4

t^2 - 16t + 64 = 64 +4 = 68

t-8 = sqr68 =8.25

t = 8+8.25 = 16.25 seconds to hit the ground