# Math Help - Quadratic model for the rocket

1. ## Quadratic model for the rocket

Equation for flight rocket is h(t) = -110t^2 + 2009.3t + 0.9 where h(t) is the height in meters above the ground after t seconds.

What is the practical domain of the function. Explain your answear.
Does the model seem realistic. Justify

One user of forum said [0, t] where h(t)=0
Well i am not pretty sure. i think that practical domain is 0=<t<=18.23
where 18.23 is a root. Please correct me if i'm wrong
And i want apologize that i didn't start new thread with another problem!!!

2. The domain is obvious for t>0. The two roots to the equation are a small negative number which we need to discard because of the t>0 condition and the other one is 18.2668s, I assume the one you mentioned. So you are correct indeed on this.

For the second part whether this is a realistic model I would say that there are some strange things about the equation. Consider the height at lift-of, it is 0.9m. This is acceptable. Consider the time for which the height is maximum. This can be calculated by considering the derivative of the equation with regards to t equal to 0. This gives approximately tm=9.1332s and thus a height of h(tm)=hm=9177m. This seems not right, going more than 9km high in 9 seconds, I could be mistaken, I'm not a rocket expert.

3. Originally Posted by Snowboarder
One user of forum said [0, t] where h(t)=0
Well i am not pretty sure. i think that practical domain is 0=<t<=18.23
where 18.23 is a root. Please correct me if i'm wrong
You and the other user are saying the same thing. h(t) = 0 means that t is a root.

-Dan