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.

The acceleration of gravity is 9.81 m/s2 . How fast was Ryan’s pitch? Answer in units of m/s

45.03756158

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

Δy = vi * t + 0.5 * a * t^2

Where:
- Δy is the vertical distance traveled (0.809 m)
- vi is the initial vertical velocity (unknown)
- t is the time of flight (unknown)
- a is the acceleration due to gravity (-9.81 m/s^2)

Since we know that the pitch traveled horizontally for a distance of 18.3 m and there is no vertical displacement in the horizontal direction, we can use the equation for horizontal motion:

Δx = vi * t

Where:
- Δx is the horizontal distance traveled (18.3 m)
- vi is the initial horizontal velocity (unknown)
- t is the same time of flight as before

By rearranging this equation, we can solve for t:

t = Δx / vi

Substituting this value for t in the vertical motion equation:

0.809 m = (Δx / vi) * t + 0.5 * a * t^2

Simplifying the equation and rearranging for vi:

vi = Δx / sqrt((2 * Δy) / a)

Plugging in the given values:

vi = 18.3 m / sqrt((2 * 0.809 m) / 9.81 m/s^2)

Calculating the expression within the square root:

vi = 18.3 m / sqrt(1.618 m / 9.81 m/s^2)

vi = 18.3 m / sqrt(0.165)

vi = 18.3 m / 0.406

vi = 45.07 m/s

Therefore, Nolan Ryan's pitch had a speed of approximately 45.07 m/s.

To calculate the speed of Nolan Ryan's pitch, we need to find the initial velocity of the pitch. We can use the equation of motion:

d = vit + (1/2)at²

where:
- d is the distance traveled by the ball (60 ft = 18.3 m)
- vi is the initial velocity (unknown)
- a is the acceleration due to gravity (9.81 m/s²)
- t is the time it takes for the ball to reach home plate

The time it takes for the ball to reach home plate can be calculated using the equation:

d = vit + (1/2)at²

Rearranging the equation:

t = √((2d) / a)

Now, substitute the given values into the equation:

t = √((2 * 18.3) / 9.81)

t ≈ 1.42 seconds

Now that we have the time, we can find the initial velocity using the equation:

vi = (d - (1/2)at²) / t

Substitute the values:

vi = (18.3 - (1/2) * 9.81 * 1.42²) / 1.42

vi ≈ 32.37 m/s

Therefore, Nolan Ryan's pitch was approximately 32.37 m/s.

distance fell= 1/2 g t^2

.809=4.9 t^2 solve for t, the time it was in the air.

howfast=distance/time= 18.3m/time