Final answer:
The acceleration of the rocket is 3.515 m/s².
Step-by-step explanation:
To determine the acceleration of the rocket, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. In this case, the net force is the force exerted by the rocket's exhaust gases, and the mass is the mass of the rocket plus the mass of the gas expelled per second.
The force exerted by the rocket's exhaust gases can be calculated using the rocket equation:
F = (m_dot * V_e)
where F is the force, m_dot is the mass flow rate of the expelled gas, and V_e is the exhaust velocity. Substituting the given values, we get:
F = (8.00 kg/s) * (2.20 × 10³ m/s) = 17.60 × 10³ N
Next, we can calculate the total mass of the rocket plus the expelled gas:
m_total = m_rocket + (m_dot * t)
where m_rocket is the mass of the rocket, m_dot is the mass flow rate of the expelled gas, and t is the time. Substituting the given values, we get:
m_total = 5000 kg + (8.00 kg/s * 1 s) = 5008 kg
Finally, we can calculate the acceleration using Newton's second law:
a = F / m_total
Substituting the calculated values, we get:
a = (17.60 × 10³ N) / (5008 kg) = 3.515 m/s²