Answer:
A ball hit from the home plate at the US Cellular field known formerly as Comiskey Park with a velocity of 114.72 ft/s at an angle of 0.85 radians, will just clear the center field fence which is 8 feet high and 400 ft distance from the home plate
Step-by-step explanation:
Here we have the US Cellular Field
Distance of center field from the home plate = 400 ft
Height of the center field fence = 8 ft
Angle of elevation, θ = 0.85 < 0.86 r = 49.3°
The formula for projectile motion is as follows
y = y₀ + v₀ × sin(θ) × t -1/2·g·t²
x = x₀ + v₀ × cos(θ) × t
Where:
x₀ = 0
y₀ = 2 ft
x = 400 ft
y = 8 ft
g = 32.2 ft/s²
Plugging the values, we have;
8 = 2 + v₀ × sin(0.85) ×t - 1/2×32.2×t² = 2 + v₀×t × sin(0.85) - 1/2×32.2×t² ...(1)
400 = 0 + v₀ × cos(0.85) × t
Solving gives v₀×t = 606.1
Substituting the value of v₀×t in equation (1) gives t= ±5.283 s
We take the +ve value for t, hence
v₀ = 606.1/t = 606.1/5.283= 114.72 ft/s
Therefore, a ball hit from the home plate at the US Cellular field with a velocity of 114.72 ft/s at an angle of 0.85 radians, will just clear the center field fence which is 8 feet high and 400 ft distance from the home plate.
Accessed from the article on "MLB Ballparks: 9 Shortest Porches in Major League Baseball" by Sean Zerillo
