In this video, I determine the vector formula for path of a projectile launched at an angle by integrating the acceleration due to gravity acting on it, and then integrating its velocity vector. When the y-component of the position vector is equal to zero (i.e. the object strikes the ground), the corresponding non-trivial time variable corresponds to the horizontal distance traveled. This distance is maximized when the launch angle is π/4 radians or 45 degrees.
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