Final answer:
To determine how high a bullet fired at 323 m/s will rise, we use the kinematic equation h = vi^2 / (2g), leading to a peak height of approximately 5324.67 meters.
Step-by-step explanation:
To calculate how high a bullet will rise when fired into the air with an initial speed of 323 m/s, we need to use the principles of projectile motion from physics. When the bullet reaches its peak height, its vertical velocity will be zero. Assuming there is no air resistance and using the acceleration due to gravity (g = 9.81 m/s2), we can use the following kinematic equation:
vf2 = vi2 - 2g * h
where vf is the final vertical velocity (0 m/s at the peak), vi is the initial vertical velocity (323 m/s), g is the acceleration due to gravity, and h is the maximum height. Rearranging the equation for h, we get:
h = vi2 / (2g)
Plugging in the values, we find:
h = (323 m/s)2 / (2 * 9.81 m/s2)
Therefore, the bullet will rise to a maximum height of approximately 5324.67 meters.