# Function of (x) word problem

• Apr 9th 2012, 11:48 PM
GAVREED2
Function of (x) word problem
A sporting airplane is flying such that its height varies with time in accordance with the formula
y = 10 + 3/(t0 + t)2, whereas its horizontal distance varies with time as x = (t0 + t)2, where t is in seconds, and x and y are in metres, t0 = 1 sec.

(a) Find the trajectory of the airplane y as a function of x.

(b) What is the function, describing the trajectory?

• Apr 10th 2012, 12:00 AM
biffboy
Re: Function of (x) word problem
In each formula make t the subject and put your answers equal to one another.
• Apr 10th 2012, 12:02 AM
Prove It
Re: Function of (x) word problem
Quote:

Originally Posted by GAVREED2
A sporting airplane is flying such that its height varies with time in accordance with the formula
y = 10 + 3/(t0 + t)2, whereas its horizontal distance varies with time as x = (t0 + t)2, where t is in seconds, and x and y are in metres, t0 = 1 sec.

(a) Find the trajectory of the airplane y as a function of x.

(b) What is the function, describing the trajectory?

You have \displaystyle \displaystyle \begin{align*} y = 10 + \frac{3}{\left(t_0 + t\right)^2} \end{align*} and \displaystyle \displaystyle \begin{align*} x = \left(t_0 + t\right)^2 \end{align*}.

Surely you can see what to substitute into the first equation...
• Apr 10th 2012, 12:19 AM
biffboy
Re: Function of (x) word problem
My method works but longer than necessary here. See ProveIt's reply for the best way.
• Apr 10th 2012, 12:33 AM
GAVREED2
Re: Function of (x) word problem
Thanks very much for both of your input!!