Question

A quarterback is asked to throw a football to a receiver that is 32.1 m away. What is the minimum speed that the football must have when it leaves the quarterback's hand?

Answer 1

The minimum speed required for a given distance is achieved when the ball is thrown at a 45 degree angle. In that case,
X = Vo^2/g

For other launch angles, the horizontal distance covered is
(Vo^2/g) * sin 2A
where A is the launch angle, measured from horizontal.

Use the first equation to solve for the initial velocity Vo.