Question

a rocket is fired upward from some initial distance above ground. Its height in feet, h, above ground, t seconds after its fired is given by h=-16t^2+96t+1792

Answer 1

What is your question? Maximum height?

Answer 2

1. What is the rocket's maximum height? ___feet
2. How long does it take for the rocket to reach its maximum height? ___seconds
3.after it is fired, the rocket reaches the ground at t=___ seconds
@yakeyglee

Answer 3

If you differentiate and find when the differential is equal to zero then you'll find the turning point and that will give you the value of t when h is greatest so plug that back into the original equation to find the maximum height.

Answer 4

ahh i dont understand :( @alrightatmaths

Answer 5

Differentiate the equation. That will give you an equation for the gradient of the line. When the gradient is equal to zero, that is a turning point and seeing as this is a negative quadratic, that will be the highest point on the graph so you'll get the value of t for which h is biggest and then you can just put it back in the original equation to get the value of h.

Answer 6

The differential is\[-32t + 96\]So when that is equal to zero then 32t = 96 and t = 3. Then put 3 back into the original equation and you get the biggest value of h.

Answer 7

okay thank you!! so does that mean after the rocket is fired it takes 6 seconds to reach the ground? or is that wrong.. lol @alrightatmaths

Answer 8

Assuming it is fired from the ground then yes.

Answer 9

But it isn't fired from the ground. It's fired from 1792 meters. So you have to factorise the equation to work out when the height is equal to zero.