To determine the time it takes for the bullet to hit the ground, we can use the equations of motion for vertical motion. The initial vertical velocity is 0 since the bullet is fired horizontally. The height from which the bullet is fired is 48 m, and the acceleration due to gravity is approximately 9.8 m/s².
Using the equation:
h = ut + (1/2)gt²,
where: h = height (48 m), u = initial vertical velocity (0 m/s), g = acceleration due to gravity (9.8 m/s²), t = time.
We can rearrange the equation to solve for time (t):
48 = (1/2)(9.8)t²
Simplifying the equation further:
t² = (48 * 2) / 9.8
t² = 96 / 9.8
t² ≈ 9.8
Taking the square root of both sides:
t ≈ √9.8
t ≈ 3.13 seconds
Therefore, it will take approximately 3.13 seconds for the bullet to hit the ground.
To calculate the range of the projectile (horizontal distance traveled), we can use the equation:
range = horizontal velocity × time.
The horizontal velocity remains constant throughout the motion and is given as 600 m/s.
range = 600 m/s × 3.13 s
range ≈ 1878 meters
Hence, the range of the projectile is approximately 1878 meters.