for a model rocket, the altitude h, in meters, as a function of time t, in secounds, is given by h=68t-8t^2.

Question

Max height:

Time of max height:

When it hits the ground:

Answer 1

1. When it is at ground level, h(t)=0. There will be 2 possible solutions to the equation taking this approach, we know we want the nonzero answer:

Solve for h(t)=0,

h(0)=68t-8t^2

=> 68t-8t^2=0 => t(68-8t)=0 => 68-8t=0 => 68=8t

t=0 s or t=68/8=17/2=8.5 s

1. Seeing the projectile motion is a quadratic, the max height time is simply one half of the total time:

4.25 s

1. Inputting the max height time into the original equation and solving for h(t) will give max height:

h(4.25)=68(4.25)-8(4.25)^2 => h(max)=144.5 m