* The Relationship: The range of a projectile is directly proportional to the square of the initial velocity, assuming a constant launch angle and neglecting air resistance. This means that if you double the initial velocity, the range will increase by a factor of four.
* Mathematical Formula: The range (R) of a projectile can be calculated using the following formula:
R = (v₀² * sin(2θ)) / g
where:
* v₀ is the initial velocity
* θ is the launch angle
* g is the acceleration due to gravity
* Inverse Proportionality: Inverse proportionality means that as one variable increases, the other decreases proportionally. In the case of projectile motion, the range increases as the initial velocity increases, not decreases.
In summary: The initial velocity and the range of a projectile are directly proportional, not inversely proportional.
