Projectile Fired from a Cannon



Problem Diagram

To prepare for a western movie set, Steve would like to find out the exact time and distance that a projectile will travel after it was fired from a cannon. It is known that the path of the projectile is given by the following parametric equations:

     x = (Ucosθ)t
     y = (Usinθ)t - 0.5gt²

In these equations, U is the initial velocity, θ is the angle above the horizontal, and g is the gravitational acceleration.

If the initial velocity of the projectile is 400 ft/s and the angle θ is 60^o. Steve would like to find out how long and how far does it take to hit the ground. Plot the trajectory of the projectile.

• Assume air resistance is negligible.
• The gravitational acceleration, g, is 32.2 ft/s².