At liftoff, a rocket has a mass of 2x10^6 kg. It expels hot gas which provides an upthrust of 3x10^7.

Find the initial accelerating of the rocket.

a = F/m = 3*10^7 / 2*10^6 = 15m/s^2.

To find the initial acceleration of the rocket, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

The net force acting on the rocket can be determined by subtracting the weight of the rocket from the upthrust it experiences during liftoff.

1. Calculate the weight of the rocket using its mass and the acceleration due to gravity, which is approximately 9.8 m/s^2.
Weight = mass * gravitational acceleration

Weight = (2x10^6 kg) * (9.8 m/s^2)

2. Subtract the weight of the rocket from the upthrust it experiences during liftoff.
Net force = upthrust - weight

Net force = (3x10^7 N) - (2x10^6 kg * 9.8 m/s^2)

3. Now, we can use Newton's second law to find the initial acceleration of the rocket.
Net force = mass * acceleration

acceleration = Net force / mass

acceleration = [(3x10^7 N) - (2x10^6 kg * 9.8 m/s^2)] / (2x10^6 kg)

By substituting the values, you can calculate the value of the initial acceleration of the rocket.