62
Lokesh Verma
·2010-04-13 21:16:25
Lets assume that the mass at any time is m(t)
and velocity is v(t)
mass at time t+dt = m+dm
Velocity at time t+dt = v+dv
External impulse during the time is (m)g dt
The change in momentum is impulse
(m+dm)(v+dv)-mv=mgdt
mdv+vdm=mgdt
m(dv/dt)+v(dm/dt)=mg
m(dv/dt)=mg-vμ
Now solve the differential equation. from time zero to time t
1
Manmay kumar Mohanty
·2010-04-13 21:28:57
vr = v, dmdt=μ , Ft ( thrust ) = vrdmdt = vμ
Net force ( Fnet ) = F - Ft
→ m dvdt = F - μv
→ (m0 + μt )dvdt = F - μv
→\int_{0}^{v}{\frac{dv}{F-\mu v}} = \int_{0}^{}t{\frac{dt}{m_{0}+\mu t}}
which gives → v = Ftm0+μt
now use equation v2 - u2 = 2aS
since u = 0
(Ftm0+μt)2 = 2gS
which gives required S.