A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 76.0 m/s2 for 1.90 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?
After t = 1.9 seconds, it attains a height of
H = (a/2) t^2 = 137.2 m
and a velocity of
V = a*t = 144.4 m/s
As the kinetic energy is converted to gravitational energy at maximum altitude, it will rise an additional distance H' given by
g*H' = V^2/2
H' = 1064 m
The maximum altitude is H + H'
I still am not understanding how to obtain the answer
To find the maximum altitude reached by the rocket, we need to first calculate its velocity when the fuel runs out and then use that velocity to find the altitude.
Given:
Acceleration (a) = 76.0 m/s^2
Time (t) = 1.90 seconds
1. Calculate the final velocity (Vf) using the formula:
Vf = Vi + (a * t)
where Vi is the initial velocity, which is 0 since the rocket starts from rest.
Vf = 0 + (76.0 m/s^2 * 1.90 s)
Vf = 144.4 m/s
2. Calculate the maximum altitude using the formula:
h = (Vf^2 - Vi^2) / (2 * a)
where Vi is again 0.
h = (144.4 m/s)^2 / (2 * 76.0 m/s^2)
h = 20816 m^2/s^2 / 152 m/s^2
h ≈ 137 meters
Therefore, the maximum altitude reached by the rocket is approximately 137 meters above the ground.
To find the maximum altitude reached by the rocket, we need to use the equations of motion and kinematic equations.
1. Start by finding the rocket's final velocity (v_final) after 1.90 seconds using the equation of motion:
v_final = v_initial + (acceleration * time)
Given:
v_initial = 0 m/s (since the rocket starts from rest)
acceleration = 76.0 m/s^2
time = 1.90 seconds
Substitute these values into the equation:
v_final = 0 + (76.0 * 1.90)
Calculate:
v_final = 144.4 m/s
2. Now, we can find the maximum altitude (h_max) using the kinematic equation that relates displacement, initial velocity, final velocity, and acceleration:
h_max = (v_final^2 - v_initial^2) / (2 * acceleration)
Given:
v_initial = 0 m/s
v_final = 144.4 m/s
acceleration = 76.0 m/s^2
Substitute these values into the equation:
h_max = (144.4^2 - 0^2) / (2 * 76.0)
Calculate:
h_max = 138.58 meters
Therefore, the maximum altitude reached by the model rocket is 138.58 meters above the ground.