A shot-putter heaves a shot from above ground level. The launch angle that will produce the longest range is less than 450°; that is, a flatter trajectory has a longer ranger range. Explain why.

One can answer the question on theoretical grounds by considering the fact the range of the ball is the horizontal distance travelled by the ball relative to its starting point. The ball moves in the projectile motion, but it also travels some extra horizontal distance after it goes down past the point from where it was released.
The figure below shows that extra horizontal distance by x :


It can be seen from this figure that the higher the angle of release (say θ ), the shorter the horizontal distance x (compare blue and red trajectories). Therefore to increase the range, the shot put must be released at a smaller angle which would be less than 45°.