The fastest recoded pitch in Major league baseball was thrown by nolan ryan in 1974. If this pitch were thrown horizontally, the ball would fall 0.809m(2.65 ft)by the time it reached home plate, 18.3m (60ft) away. how fast was ryans pitch?
To determine the speed of Nolan Ryan's pitch, we need to use the distance the ball traveled and the time it took to reach its destination. In this case, we are given the distance the ball fell, which is 0.809 meters (2.65 feet), and the horizontal distance it traveled, which is 18.3 meters (60 feet).
We can use the equation of motion to calculate the time it took for the ball to reach home plate. The equation we'll use is:
s = ut + (1/2)at^2
Where:
s = distance fallen (0.809 m)
u = initial velocity in the vertical direction (unknown)
t = time taken (unknown)
a = acceleration due to gravity (-9.8 m/s^2, assuming downward is negative)
Since the ball is thrown horizontally, the initial vertical velocity (u) is zero, and the equation becomes:
0.809 = (1/2)(-9.8)t^2
Simplifying the equation:
0.809 = -4.9t^2
To solve for t, divide both sides of the equation by -4.9:
0.809 / -4.9 = t^2
t^2 = -0.1657
Since time cannot be negative, we discard the negative square root, and we are left with:
t ≈ 0.406 seconds
Now that we know the time, we can calculate the speed using the horizontal distance traveled (18.3 m). The formula to find speed is:
speed = distance / time
speed = 18.3 m / 0.406 s
Calculating this:
speed ≈ 45.07 m/s
Therefore, Nolan Ryan's pitch speed was approximately 45.07 meters per second.
To find the speed of Nolan Ryan's pitch, we can use the formula: speed = distance / time.
First, let's convert the distance from feet to meters:
Distance = 60 ft = 18.3 m
Next, we need to find the time it takes for the pitch to reach home plate. Since the pitch was thrown horizontally, we can consider it as a projectile motion with only the effect of gravity acting on it. The vertical displacement (fall) of the ball can help us calculate the time.
Vertical displacement = 0.809 m
Using the equation of motion, we can relate the vertical displacement, time, and acceleration due to gravity:
Vertical displacement = (1/2) * g * t^2
0.809 = (1/2) * 9.8 * t^2
0.809 = 4.9 * t^2
t^2 = 0.809 / 4.9
t^2 = 0.165
t = sqrt(0.165)
t ≈ 0.406 seconds
Now we can calculate the speed of the pitch:
Speed = Distance / Time
Speed = 18.3 / 0.406
Speed ≈ 45.08 m/s
Therefore, Nolan Ryan's pitch was approximately 45.08 m/s (meters per second).