a shell has an initial velocity of 450 feet per second, what is the maximum height the shell reaches?
To find the maximum height reached by the shell, we need to use kinematic equations. In this case, we can use the equation for vertical motion known as the projectile motion equation:
h = (v^2 * sin^2(theta)) / (2 * g),
where:
h is the maximum height,
v is the initial velocity (450 feet per second),
theta is the angle of projection (which is not mentioned in the question),
and g is the acceleration due to gravity (which is approximately 32.2 feet per second squared).
Since the angle of projection is not given, we assume it to be the maximum possible angle of 90 degrees (which corresponds to firing the shell straight up). Therefore, the equation simplifies to:
h = (v^2) / (2 * g).
Plugging in the values:
h = (450^2) / (2 * 32.2) = 316,406.84 / 64.4 ≈ 4,906.8 feet.
So, the maximum height the shell reaches is approximately 4,906.8 feet.