Question

Determine whether the following statements are true and give an explanation or counterexample. If you double the initial speed of a projectile, its range also doubles (assume no forces other than gravity act on the projectile)

Answer 1

Doubling the initial speed of a projectile does not double its range. The range of a projectile is determined by both the initial speed and the angle of projection.

Step-by-step explanation:

The initial velocity of a projectile affects its range. Doubling the initial speed of a projectile does not result in doubling its range. The range is dependent on both the initial speed and the angle at which the projectile is fired.

The range equation for a projectile on level ground with negligible air resistance is given by R = (vo^2 * sin2θ) / g, where vo is the initial speed, θ is the angle of projection, and g is the acceleration due to gravity.

For a fixed initial speed, the maximum range is obtained at an angle of 45°, assuming no air resistance. However, for every initial angle except 45°, there are two angles that give the same range, and the sum of those angles is always 90°.