Understanding the Formula
The horizontal range (R) of a projectile launched at an angle (θ) with an initial velocity (v) is given by:
R = (v² * sin(2θ)) / g
Where:
* g is the acceleration due to gravity (approximately 9.8 m/s²)
Doubling the Initial Velocity
If you double the initial velocity (v), the formula becomes:
R = ((2v)² * sin(2θ)) / g
Simplifying:
R = (4v² * sin(2θ)) / g
The Result
Notice that the new range is four times (4 times) the original range.
In conclusion: Doubling the initial velocity of a projectile will quadruple its horizontal range, assuming the launch angle remains constant.
