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

  • #1

Homework Statement

A cannon shoots a ball at an angle [itex]\theta[/itex] 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).

Homework Equations

[itex]\frac{dx}{dt}[/itex] = Vocos([itex]\theta[/itex])

[itex]\frac{dy}{dt}[/itex] = Vosin([itex]\theta[/itex]) - gt

The Attempt at a Solution

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

x(t) = Vocos([itex]\theta[/itex])t

y(t) = Vosin([itex]\theta[/itex])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?
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  • #2
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.

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