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Range of Flight Formula:
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The Range of Flight Formula calculates the horizontal distance a projectile travels when launched at a specific angle with a given initial velocity, assuming ideal conditions (no air resistance, constant gravity).
The calculator uses the projectile motion range formula:
Where:
Explanation: The formula calculates maximum horizontal distance achieved by a projectile launched from ground level, reaching maximum range at 45° launch angle.
Details: Range calculation is essential in physics, engineering, ballistics, sports science, and military applications for predicting projectile trajectories and optimizing launch parameters.
Tips: Enter initial velocity in m/s and launch angle in degrees (0-90°). The calculator automatically converts degrees to radians and computes the range. Maximum range occurs at 45°.
Q1: Why does maximum range occur at 45°?
A: At 45°, the sine function sin(2θ) reaches its maximum value of 1, providing optimal balance between horizontal and vertical velocity components.
Q2: What are typical velocity ranges for different projectiles?
A: Baseball: 30-45 m/s, Soccer ball: 20-35 m/s, Arrow: 50-90 m/s, Bullet: 250-900 m/s depending on caliber and firearm.
Q3: Does air resistance affect the actual range?
A: Yes, this formula assumes ideal conditions. In reality, air resistance significantly reduces range, especially for lightweight or high-velocity projectiles.
Q4: Can this formula be used for different gravitational fields?
A: Yes, simply adjust the g value for different planets (Moon: 1.62 m/s², Mars: 3.71 m/s²).
Q5: What if the launch and landing heights are different?
A: This formula assumes same launch and landing height. For different heights, more complex equations accounting for vertical displacement are needed.