Final answer:
By calculating the time it takes for a baseball to fall vertically 0.809 meters under gravity, we can determine the horizontal velocity of Nolan Ryan's pitch over an 18.3-meter distance, revealing it to be 45.07 m/s.
Step-by-step explanation:
To find out how fast Nolan Ryan's pitch was, we can use the kinematic equations for projectile motion. Since the question states that the baseball falls 0.809 meters by the time it reaches home plate 18.3 meters away, we are only considering the vertical motion to calculate the time it takes for the ball to drop 0.809 meters due to gravity. The horizontal motion will then reveal the speed of Ryan's pitch.
The equation we need for the vertical motion is s = ut + 0.5at2, where s is the displacement (0.809 m), u is the initial vertical velocity (0 m/s since the ball is thrown horizontally), a is the acceleration due to gravity (9.81 m/s2), and t is the time.
After calculating the time t, we can use it along with the horizontal distance d to find out the horizontal velocity: v = d/t. This will give us the speed of the pitch.
Step 1: Calculate the time it takes to fall 0.809 meters:
0.809 = 0 * t + 0.5 * 9.81 * t2
t2 = (2 * 0.809) / 9.81
t2 = 0.1646
t = 0.406 seconds
Step 2: Calculate the horizontal velocity:
v = 18.3 / 0.406
v = 45.07 m/s