A rocket moves in the absence of external forces by ejecting a steady jet with velocity u constant relative to the rocket. Find the velocity v of the rocket at the moment when its mass is equal to m, if at the initial moment it possessed the mass `m_0` and its velocity was equal to zero. Make use of the formula given in the foregoing problem.

Explanation

According to the question, `vecF=0` and `mu=-dm//dt` so the equation for this system becomes,
`m(dvecv)/(dt)=(dm)/(dt)vecu`
As `dvecvuarrdarrvecu` so, `mdv=-udm`.
Integrating within the limits:
`1/u underset(0)overset(v)intdv=-underset(m_0)overset(m)int(dm)/(m)` or `v/u=1n(m_0)/(m)`
Thus, `v=u1n(m_0)/(m)`
As `dvecvuarrdarrvecu`, so in vector form `vecv=-vecu1n(m_0)/(m)`