in the first second of its flight, a rocket ejects 1/60 of its mass with a velocity of 2400 m/s the acceleration of the rocket is
a = 24m/s/s = 24m/s^2.
Answer is 2400/60 = 40 meter per second square
To find the acceleration of the rocket, we first need to understand the principle of conservation of momentum. According to this principle, the total momentum before and after an event should remain the same if no external forces are acting.
In this case, the rocket ejects a certain mass with a velocity. Let's call the initial mass of the rocket "M" and the velocity of ejection "v". The mass ejected can be calculated using the formula:
Mass ejected = (1/60) * M
The momentum before ejection is given by:
Initial momentum = M * 0 (since the rocket is at rest initially)
The momentum after ejection can be calculated as:
Momentum after ejection = (M - mass ejected) * v
Now, according to the conservation of momentum, the initial and final momentum should be equal. Therefore:
Initial momentum = Momentum after ejection
0 = (M - mass ejected) * v
Let's substitute the values given:
0 = (M - (1/60)M) * 2400
Simplifying further:
0 = (59/60)M * 2400
Now, we can solve for M:
0 = (59/60)M * 2400
0 = (59/60)M * 2400 / (59/60)
0 = M * 2400
M = 0
Since the initial mass of the rocket (M) is zero, it means that there is no rocket to begin with. Therefore, there is no concept of acceleration for this scenario.