Posted by Jake on Thursday, October 25, 2012 at 10:23pm.
A rocket ascends from rest in a uniform gravitational field by ejecting exhaust with constant speed u.
Assume that the rate at which mass is expelled is given by dm/dt=mk, where m is the instantaneous mass of the rocket and k is a cosntant, and that the rocket is retarded by air resistance with a force bv where b is a constant. find the velocity of the rocket as a function of time.
I have worked it down to the last step but am having trouble finishing the integration to find v(t).
F_net = F_thrust  F_grav  F_air.resist
ma = (dp/dt)  mg  bv
(dv/dt) = (uk  g)  (bv/m)
m = m_o*e^kt > not sure if this part is right??
so (dv/dt) = (uk  g)  b*m_o*e^kt*v
v = dx/dt so multiply by dt to get the integration equation of:
dv = (ukg)dt  b*m_o*e^kt*dx
my attempt so far:
v(t) = (ukg)t  ????
***I am stuck on integrating the:
b*m_o*e^kt*dx

Physics  Jake, Thursday, October 25, 2012 at 10:26pm
I think that the answer comes out to be
v(t)=(ukg)t  b*m_o*(e^kt)*x(t)

Physics  Jake, Thursday, October 25, 2012 at 10:28pm
because b and m_o are constants and i believe that e^kt is taken as a constand as well. Leaving dx to be integrated between 0 and x(t).
am i correct? more opinions welcomed please
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