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
To determine the minimum safe height for birds around baseball stadiums, we need to consider the trajectory of a baseball hit at a 45-degree angle and its maximum distance.
1. First, let's calculate the horizontal distance covered by a baseball hit at a 45-degree angle.
- We know that the longest home runs in baseball land about 500 feet from home plate, which is equal to 152.4 meters.
- Since the ball follows a parabolic trajectory, the horizontal distance is equal to the total distance traveled by the ball.
- Using basic trigonometry, we can find the horizontal distance (d) as: d = 152.4 m.
2. Next, we need to determine the vertical distance (h) covered by the baseball at a 45-degree angle.
- Since the trajectory is symmetric, the highest point of the trajectory will be halfway between the launch point and the landing point.
- Using trigonometry, we can find the vertical distance (h) as: h = d * sin(45°).
3. Now, let's calculate the minimum safe height for birds by considering the vertical distance covered by the baseball.
- To ensure the safety of birds, we want to set the minimum safe height higher than the highest point of the baseball's trajectory (h).
- Adding a safety margin, let's consider a minimum safe height of 10 meters above the highest point of a baseball's trajectory.
- Therefore, the minimum safe height for birds would be: minimum safe height = h + 10 meters.
By calculating the horizontal distance and vertical distance covered by a baseball hit at a 45-degree angle, and adding a safety margin, we can determine the minimum safe height for birds around baseball stadiums.