To determine the maximum height of flight for a bottle rocket shot straight up in the air, we can use basic principles of projectile motion. We assume that the rocket's initial velocity is 30 m/s and air resistance is ignored.
In the absence of air resistance, the rocket's motion can be divided into two phases: the upward phase and the downward phase. At the maximum height, the rocket's vertical velocity will momentarily become zero before it starts descending.
We can use the kinematic equation for vertical motion to calculate the maximum height:
v_f^2 = v_i^2 + 2ad
Where: v_f is the final velocity (which becomes 0 at the maximum height) v_i is the initial velocity (30 m/s) a is the acceleration (due to gravity, approximately -9.8 m/s^2) d is the displacement (maximum height)
Rearranging the equation:
0 = (30 m/s)^2 + 2(-9.8 m/s^2)d
900 m^2/s^2 = -19.6 m/s^2 d
d = 900 m^2/s^2 / -19.6 m/s^2
d ≈ -45.92 m
Since distance cannot be negative in this context, we take the magnitude of the displacement:
d ≈ 45.92 m
Therefore, the maximum height of flight for the bottle rocket is approximately 45.92 meters.