The fastest recorded pitch was clocked at 160 km/h. If a pitch were thrown
horizontally with this velocity, how far would the ball fall vertically by the time it
reached home plate, 20 m away?
To solve this problem, we can use the equation for vertical displacement under gravity:
d = 0.5 * g * t^2
Where:
d = vertical displacement
g = acceleration due to gravity (9.81 m/s^2)
t = time of flight
First, we need to find the time it takes for the pitch to travel 20 m horizontally at a velocity of 160 km/h. We can convert the velocity from km/h to m/s:
160 km/h = 160,000 m/3600 s = 44.44 m/s
Now, we can calculate the time of flight:
t = distance / velocity
t = 20 m / 44.44 m/s
t = 0.45 s
Next, we can calculate the vertical displacement by plugging the time into the equation:
d = 0.5 * 9.81 m/s^2 * (0.45 s)^2
d = 0.5 * 9.81 m/s^2 * 0.2025 s^2
d = 0.5 * 9.81 m/s^2 * 0.2025 s^2
d = 0.5 * 1.98 m
d = 0.99 m
Therefore, by the time the pitch reaches home plate 20 m away, it would have fallen vertically by approximately 0.99 meters.