Maximize the Range: The Optimal Cannon Angle
A ball is fired from a cannon at an angle θ from the horizontal at a speed v0 .
Starting from x = 0 and y = 0 the ball will initially climb and then fall back to
the ground y = 0 with acceleration due to gravity −g. The horizontal distance it
travels is called the range.
1. Find the ball’s initial horiz and vert velocity vx and vy in terms of v0 and θ.
2. Find the horiz and vert positions x(t) and y(t) in terms of g, t, v0 and θ.
3. Find the time tf when it hits the ground and the range xmax = x(tf ).
4. For what value of θ is the range maximized?
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