Newton's 2nd Law says $\vec{F}= \frac{d\vec{p}}{dt}$ .

In a constant mass system this becomes $\vec{F}=m\vec{a}$. Answers to why $F=ma$ can be found here.

However, in a variable mass sytem (see derivation) Newton's 2nd law still applies and it becomes ${\mathbf {F}}_{{{\mathrm {ext}}}}+{\mathbf {v}}_{{{\mathrm {rel}}}}{\frac {{\mathrm {d}}m}{{\mathrm {d}}t}}=m{{\mathrm {d}}{\mathbf v} \over {\mathrm {d}}t}$ . What experimental evidence is there for this (both that Newton's law will apply and/or that this equation is correct)?