Question: In the first second of its flight, a rocket ejects 1/60 of its mass with a relative velocity of 2073 m/s. What is the initial acceleration of the rocket?

Solution:

To determine the initial acceleration of the rocket, we can use the principle of conservation of momentum.

Step 1: Identify Given Information
- Mass of the rocket: M
- Mass ejected in the first second: 1/60 * M
- Relative velocity of the ejected mass: 2073 m/s

Step 2: Apply Conservation of Momentum
According to the principle of conservation of momentum, the total momentum before and after the ejection must be the same.

The total momentum before ejection is given by:
M_initial * V_initial, where V_initial is the initial velocity of the rocket.

The total momentum after ejection is given by:
(M - (1/60 * M)) * V_final, where V_final is the final velocity of the rocket.

Since the ejection happens in the first second, the final velocity can be assumed to be the initial velocity of the rocket.

Step 3: Equate the Momenta
Setting the total momentum before ejection equal to the total momentum after ejection, we have:
M_initial * V_initial = (M - (1/60 * M)) * V_initial

Step 4: Solve for Initial Acceleration
To find the initial acceleration, we need to relate it to the initial velocity. Using the equation of motion, we have:
V_final = V_initial + a * t

Since the final velocity is assumed to be the initial velocity, we can rewrite the equation as:
V_initial = V_initial + a * t

Simplifying the equation, we get:
0 = a * t

Therefore, the initial acceleration, a, is zero.

Conclusion:
The initial acceleration of the rocket is 0 m/s².