Newton\'s second law F=ma can be written F=d/dt (mv). When the mass of an object

Question

Newton's second law F=ma can be written F=d/dt (mv). When the mass of an object is variable, this latter formulation is used. The mass m(t) of a rocket launched upward changes as its fuel is consumed. If v(t) denotes its velocity at any time, it can be shown that

-mg=m dv/dt - V dm/dt, where V is the constant velocity of the exhaust gases relative to the rocket. Use the last equation to find the differential equation for v if it is known that m(t)=m0 - at and V=-b where m0, a and b are constants.

Explanation / Answer

F= mg gravitational pull

F= d/dt(m.v) ...................... by definition

F= v*d/dt(m)+m*d/dt(v)

d/dt(v)=-(V*d/dt(m)+m)/m..

where m = mass

V= constant exhaust gases

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