Final answer:
The ball will hit the ground approximately 1.96 meters away from the projectile launcher.
Step-by-step explanation:
The distance that the ball will travel horizontally can be calculated using the time it takes for the ball to hit the ground. Since the ball is launched horizontally, its initial vertical velocity is 0 m/s. The time it takes for the ball to hit the ground can be found using the formula t = √(2h/g), where h is the height of the projectile launcher and g is the acceleration due to gravity (approximately 9.8 m/s²).
In this case, the height of the projectile launcher is given as 1.2 m. Plugging in the values, we get t = √(2(1.2)/9.8) ≈ 0.49 s.
Once we have the time, we can use the horizontal velocity and the time to find the horizontal distance traveled by the ball, which is given by d = v × t, where v is the horizontal velocity. Plugging in the values, we get d = 4 m/s × 0.49 s ≈ 1.96 m. Therefore, the ball will hit the ground approximately 1.96 meters away from the projectile launcher.