Final answer:
To calculate the percent change in velocity due to gravity when the ball reaches the batter, we can use the concept of projectile motion. By finding the vertical component of velocity using the equation for projectile motion and the time of flight, we can calculate the percentage change in velocity.
Step-by-step explanation:
To calculate the percent change in velocity due to gravity when the ball reaches the batter, we can use the concept of projectile motion. When the ball is pitched, its initial velocity is 130 km/h horizontally. The pull of gravity acts vertically downwards, but it does not change the magnitude of the horizontal velocity. So, the change in velocity due to gravity would only affect the vertical component of velocity.
To find the vertical component of velocity, we can use the equation for projectile motion:
Vy = V0y + (-g)t
Where Vy is the final velocity in the y-direction (vertical direction), V0y is the initial velocity in the y-direction, g is the acceleration due to gravity (-9.8 m/s2), and t is the time of flight.
Since the initial velocity in the y-direction is 0 m/s (as the ball is pitched horizontally), the equation simplifies to:
Vy = (-g)t
Now, we can find the time it takes for the ball to reach the batter using the equation:
d = Vxt
Where d is the horizontal distance (18 m) and Vx is the horizontal velocity (130 km/h, converted to m/s).
Once we have the time of flight, we can substitute it into the equation for Vy to find the final vertical velocity. Finally, we can calculate the percentage change in velocity by taking the difference between the initial and final velocities and dividing it by the initial velocity, multiplied by 100.