A mother rocket fired from the ground last year’s eve ejects 25% of its mass 2.0 at the at the rate if so m/s in the first second of its flight. Find the initial acceleration of the mother rocket.

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To find the initial acceleration of the mother rocket, we need to first determine the rate of change in velocity (velocity change per unit time) based on the mass ejection. We can then use this information to calculate the initial acceleration.

Let's break down the given information:
- The rocket ejects 25% of its mass.
- The mass is ejected at a rate of 2.0 kg/s.
- The velocity change of the ejected mass is given as m/s.

First, let's find the mass that is being ejected per second:
Mass ejected per second = 25% of the rocket's mass
Let's denote the mass of the rocket as M.
Mass ejected per second = (25/100) * M

Now, we are given that the rate of ejection is 2.0 kg/s.
Therefore, (25/100) * M = 2.0 kg/s

We can solve this equation to find the mass of the rocket (M):
M = (2.0 kg/s) / (25/100)
M = (2.0 kg/s) * (100/25)
M = 8.0 kg

Now that we have the mass of the rocket, we can determine the net force acting on the rocket using Newton's second law of motion:
Force = (Mass of ejected gas) * (Acceleration of ejected gas)
Force = (25/100) * M * (dv/dt)

The net force acting on the rocket can be calculated as follows:
Net Force = (Mass of Rocket + Mass of ejected gas) * (Acceleration of Rocket)
Net Force = (M + (25/100) * M) * (Acceleration of Rocket)

The mass of the rocket can be expressed as:
Mass of Rocket = M

Now we can write the equation for the net force:
(M + (25/100) * M) * (Acceleration of Rocket) = (25/100) * M * (dv/dt)

Let's simplify this equation:
(1 + 0.25) * (Acceleration of Rocket) = 0.25 * (dv/dt)

1.25 * (Acceleration of Rocket) = 0.25 * (dv/dt)

Finally, we can find the initial acceleration of the mother rocket by dividing both sides of the equation by 1.25:
Acceleration of Rocket = (0.25/1.25) * (dv/dt)

Acceleration of Rocket = 0.2 * (dv/dt)

Therefore, the initial acceleration of the mother rocket is 0.2 times the rate of change in velocity of the ejected mass.