Eliminating in Parametrics

[wednesdayweekb]

A ball is struck at ground level and projected with a speed of 16 m/s-at a FIXED angle θ to the horizontal.
The parametric equations of the path of the ball are given by

? = 16?????,
? = 16????? − 5?²

(i) By eliminating t show that the Cartesian equation of the path can be written as a quadratic in tan θ.

I can eliminate the 16t's but I cant for the life of me get rid of the 5t²

I tried
x/y = tan? - (5t²)/16tcos? but where from there I have no clue. Any help hugely appreciated

 

[HallsofIvy]

Do you see that, from \(\displaystyle x= 16t cos(\theta)\), \(\displaystyle t= \frac{x}{16 cos(\theta)}\)?

And that you can use that to eliminate both \(\displaystyle 16t\) and \(\displaystyle 5t^2\)?

 

[topsquark]

How about
[math]t = \dfrac{x}{16 ~ cos( \theta )}[/math] from the first equation, then

[math]y = 16 \left ( \dfrac{x}{16 ~ cos( \theta )} \right ) ~ sin( \theta ) - 5 \left ( \dfrac{x}{16 ~ cos( \theta )} \right ) ^2[/math]
Now simplify.

-Dan