# Trajectory of a ball

1. Sep 24, 2013

### majinsock

1. The problem statement, all variables and given/known data

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

a) Neglecting air resistence, 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).

2. Relevant equations

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

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

3. The attempt at a solution

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

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

y(t) = Vosin($\theta$)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?

Last edited: Sep 24, 2013
2. Sep 24, 2013

### 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.