Ball Trajectory: Solve for x(t) & y(t) & y(x)

[majinsock]

Homework Statement

A cannon shoots a ball at an angle $\theta$ above the horizontal ground

a) Neglecting air resistance, find the ball's position (x(t) and y(t)) as a function of time.

b) Take the above answer and find an equation for the ball's trajectory y(x).

Homework Equations

$\frac{dx}{dt}$ = V_ocos($\theta$)

$\frac{dy}{dt}$ = V_osin($\theta$) - gt

The Attempt at a Solution

Okay, so I integrated both sides of both equations and ended up with:

x(t) = V_ocos($\theta$)t

y(t) = V_osin($\theta$)t - 0.5gt²

which I'm pretty sure solves part a), but I'm having a lot of trouble finding a function of y in terms of x for part b). I tried messing around with some trigonometric identities but I get nowhere. Any tips?

 

[Saitama]

Try to find t in terms of x or y from one of the equations you found for part a. Substitute that in the other equation.