Problem: The problem states that a rocket fired from the earth surface ejects 1% of its mass at a speed of 2000m/s in the first second. We need to find out the average acceleration of the rocket in the first second.

Solution:

We can use the concept of conservation of momentum to solve this problem. According to the conservation of momentum, the total momentum of a system remains constant if no external force acts on it.

Let's assume that the initial mass of the rocket is m and its initial velocity is u. After ejecting 1% of its mass at a speed of 2000m/s, the remaining mass of the rocket is 0.99m and its velocity is u'. We can write the conservation of momentum equation as:

m * u = 0.99m * u' + 0.01m * 2000

Simplifying the above equation, we get:

u' = u - (2000/99)

The average acceleration of the rocket in the first second can be calculated as follows:

Average acceleration = (Change in velocity) / (Time taken)

We know that the rocket ejects 1% of its mass at a speed of 2000m/s in the first second. Therefore, the change in velocity of the rocket in the first second is u' - u. So, the average acceleration of the rocket in the first second can be calculated as:

Average acceleration = (u' - u) / 1

Substituting the value of u' in the above equation, we get:

Average acceleration = [(u - (2000/99)) - u] / 1

Simplifying the above equation, we get:

Average acceleration = - (2000/99)

Converting the above value to m/s², we get:

Average acceleration = - 20.20 m/s²

Since the rocket is moving upwards, we take the magnitude of the above value to get the final answer:

Average acceleration = 20 m/s² (approx)

Therefore, the average acceleration of the rocket in the first second is 20 m/s².

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