- #1

Gogsey

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remaining mass m. Show that, if k is very large, it agrees with the result derived in class (without gravity).

Ok, so i have already proved the first part.

P(t)=mv and P(t+dt) = (m+dm)(v+dv)-dM(v-v(ext))

=mv+vdm+dmv(ext)

The a couple of steps later we get: -mgdt=mdv+(ext)(dm/dt)

so we get -mg=mdv/dt -kv(ext), where -k=dm/dt

and therefore mdv/dt=kv(ext) - mg.

Ok, so I'm a little stuck on the second part. Not really sure where to start off. Any hints?