Physics
posted by Dan .
Every once in a while a bird will get hit by a baseball during a baseball game. The longest home runs in baseball land about 500 feet (which is 152.4 meters) from home plate. If these balls leave the bat at a 45 degree angle to maximize their distance, what is the minimum safe height in meters for birds around baseball stadiums?

The maximum elevation of a ball hit at a 45 degree angle is half of the range.
Range = Vo^2/g for 45 degree initial angle = 500 feet
Max height = (Vo*sin45)^2/g = Vo^2/(2 g)
= 250 feet 
Range = [2*(Vo^2)]/g = 500 ft
Max. height = (Vo^2)/(2*g) = 125 ft or 38.1 m