To determine how far from the throwing point the baseball will attain its original level, we can analyze the projectile motion of the baseball. We'll assume no air resistance and consider the acceleration due to gravity as 9.8 m/s².
Given: Initial velocity (magnitude): 100 m/s Launch angle: 30° above the horizontal
To find the horizontal distance traveled by the baseball, we need to calculate the time it takes to reach its original level.
First, let's decompose the initial velocity into its horizontal and vertical components. The horizontal component (Vx) remains constant throughout the motion, while the vertical component (Vy) changes due to the effect of gravity.
Vx = V * cosθ Vy = V * sinθ
where V is the initial velocity magnitude and θ is the launch angle.
Vx = 100 m/s * cos(30°) = 100 m/s * √3/2 ≈ 86.6025 m/s Vy = 100 m/s * sin(30°) = 100 m/s * 1/2 = 50 m/s
The time taken to reach the original level can be found using the equation:
t = Vy / g
where g is the acceleration due to gravity (9.8 m/s²).
t = 50 m/s / 9.8 m/s² ≈ 5.102 seconds
Now, we can calculate the horizontal distance (R) traveled by the baseball using the equation:
R = Vx * t
R = 86.6025 m/s * 5.102 s ≈ 441.34 meters
Therefore, the baseball will attain its original level approximately 441.34 meters from the throwing point.