To find the greatest possible range of a projectile, we need to determine the horizontal distance it covers before hitting the ground.
The range of a projectile can be calculated using the formula:
Range = (Initial velocity^2 * sin(2θ)) / g
where:
- Initial velocity is the magnitude of the initial velocity of the projectile (40 m/s).
- θ is the launch angle (45 degrees).
- g is the acceleration due to gravity (approximately 9.8 m/s^2).
Let's substitute the given values into the formula:
Range = (40^2 * sin(2 * 45°)) / 9.8
Calculating further:
Range = (1600 * sin(90°)) / 9.8 = (1600 * 1) / 9.8 ≈ 163.27 meters
Therefore, the greatest possible range of the ball when air resistance is considered to be negligible is approximately 163.27 meters.