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/(*t*0 + *t*)2, whereas its horizontal distance varies with time as *x *= (*t*0 + *t*)2, where *t *is in seconds, and *x *and *y *are in metres, *t*0 = 1 sec.

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

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

Re: Function of (x) word problem

In each formula make t the subject and put your answers equal to one another.

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/(*t*0 + *t*)2, whereas its horizontal distance varies with time as *x *= (*t*0 + *t*)2, where *t *is in seconds, and *x *and *y *are in metres, *t*0 = 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...

Re: Function of (x) word problem

My method works but longer than necessary here. See ProveIt's reply for the best way.

Re: Function of (x) word problem

Thanks very much for both of your input!!