The fastest recorded pitch in Major League Baseball was thrown by Nolan Ryan in 1974. If this pitch were thrown horizontally, the ball would fall 0.809 m (2.65 ft) by the time it reached home plate, 18.3 m (60 ft) away. How fast was Ryan’s pitch? (See Sample Problem 3D)

To find the speed of Nolan Ryan's pitch, we can use the equation for horizontal motion:

distance = speed × time

In this case, the distance is 18.3 m, and we need to find the speed. The time it takes for the pitch to reach home plate can be calculated by dividing the distance by the horizontal component of the velocity.

Since the pitch falls 0.809 m (2.65 ft) in this horizontal distance, we can say that the vertical displacement is -0.809 m (negative because it falls downwards).

We can use the equation for vertical motion to find the time taken:

vertical displacement = initial vertical velocity × time + 0.5 × acceleration × time^2

Since the pitch was thrown horizontally, the initial vertical velocity is 0 m/s, and the acceleration is gravity, which is approximately -9.8 m/s^2.

Substituting the values into the equation:

-0.809 m = 0 × time + 0.5 × (-9.8 m/s^2) × time^2

Simplifying the equation:

-0.809 m = -4.9 m/s^2 × time^2

Divide both sides by -4.9 m/s^2:

time^2 = 0.809 m / 4.9 m/s^2

time^2 ≈ 0.1653 s^2

Taking the square root of both sides:

time ≈ √0.1653 s

time ≈ 0.406 s

Now that we know the time, we can use the equation for horizontal motion to find the speed:

distance = speed × time

18.3 m = speed × 0.406 s

Divide both sides by 0.406 s:

speed ≈ 18.3 m / 0.406 s

speed ≈ 45.05 m/s

So, Nolan Ryan's pitch was approximately 45.05 m/s fast.