The range of a projectile will be quadrupled (increased by four times) if its initial speed is doubled.
Explanation:
The range of a projectile is determined by the following equation:
* R = (v₀² * sin(2θ)) / g
Where:
* R is the range
* v₀ is the initial speed
* θ is the launch angle
* g is the acceleration due to gravity
Analysis:
* v₀²: When you double the initial speed (v₀), the square of the initial speed (v₀²) becomes four times larger.
* sin(2θ): The launch angle remains the same, so sin(2θ) doesn't change.
* g: Acceleration due to gravity remains constant.
Conclusion:
Since the range is directly proportional to the square of the initial speed, doubling the initial speed will result in a fourfold increase in the range.
