A woman using a rocket pack hovers near a balcoy. The mass of the woman with gea

Question

A woman using a rocket pack hovers near a balcoy.  The mass of the woman with gear is 100 kg and her tanks hold 50 kg of rocket fuel.  The exhaust velocity of the fuel is 2200 m/s.  Find a) What rate of fuel consumption is required for hovering, b) If k remains constant, what is the woman's velocity whe she runs out of fuel?  Set up an integral to find how far the woman goes upward during the time her fuel is burning.

I got part a of this using dm/dt = (m*g)/(exhaust velocity) = -.67 kg/s.  I don't know how to solve b and c given the rocket equation.  Thanks in advance.

Explanation / Answer

if rate is constant, mdot*v + m*vdot = -mg where mdot = -0.67, m= 150 - 0.67t

which gives -0.67 v + (150 -0.67t)a = -(150 -0.67t)*9.8

you solve it like a linear ODE of the type y' + p(x)y = q(x)

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