To analyze the motion of the baseball, we can break down its initial velocity into horizontal and vertical components.
1. Horizontal Component:
The horizontal component of the velocity remains constant throughout the motion. We can find the horizontal component using trigonometry. The formula is:
Horizontal component = initial velocity * cos(angle)
In this case, the initial velocity is 25 m/s, and the angle above the horizontal is 30°. Substituting these values into the formula:
Horizontal component = 25 m/s * cos(30°)
Horizontal component = 25 m/s * √3/2
Horizontal component ≈ 21.65 m/s
2. Vertical Component:
The vertical component of the velocity changes due to the effect of gravity. Initially, the baseball is moving upward, reaches its peak, and then falls downward. We can find the initial vertical component using trigonometry. The formula is:
Vertical component = initial velocity * sin(angle)
Using the same values as before:
Vertical component = 25 m/s * sin(30°)
Vertical component = 25 m/s * 1/2
Vertical component = 12.5 m/s
Since the baseball was initially hit, we assume no initial vertical displacement (no height difference). Thus, the initial vertical velocity is 12.5 m/s upwards.
By breaking down the initial velocity into horizontal and vertical components, we can analyze different aspects of the baseball's motion, such as its range, time of flight, and maximum height. If you have any specific questions about these aspects, please let me know, and I'll be glad to provide more information.