Formula:
* Range (R) = (v₀² * sin(2θ)) / g
Where:
* v₀ is the initial velocity of the projectile
* θ is the launch angle (the angle at which the projectile is launched)
* g is the acceleration due to gravity (approximately 9.8 m/s²)
Assumptions:
* The projectile is launched on a horizontal surface.
* Air resistance is negligible.
Understanding the Formula:
* v₀² * sin(2θ): This term represents the initial horizontal velocity squared multiplied by the sine of twice the launch angle. This factor determines how far the projectile will travel horizontally.
* g: This represents the acceleration due to gravity, which pulls the projectile downwards, ultimately determining how long it stays in the air.
Key Points:
* Maximum Range: The maximum range is achieved when the launch angle is 45 degrees. This is because sin(90°) = 1, maximizing the numerator of the formula.
* Launch Angle: The range is affected by the launch angle. Changing the launch angle will change the time the projectile spends in the air, thus affecting the horizontal distance it travels.
Example:
If a projectile is launched with an initial velocity of 20 m/s at an angle of 30 degrees, its range can be calculated as follows:
* R = (20² * sin(2 * 30°)) / 9.8
* R = (400 * sin(60°)) / 9.8
* R ≈ 35.3 meters
Therefore, the projectile would travel approximately 35.3 meters horizontally.
