A toy rocket is launched in the vertical direction. The following is given: the initial mass of the rocket is m0=60g; the mass of the fuel is mF=6g; the exhaust velocity is u; the mean thrust is T=5N; the burnout time (time it takes to burn all fuel) is tB=0.8s Assume no air drag and that the fuel burns at a constant rate. Derive the equation for maximum height and then obtain a numerical value form the data above.


 m(dv/dt) = -mg + uα        (1)

m(dv/dt) = -mg                (2)

Where α is the mass flow rate of exhaust (or dm/dt). I have already computed α and it should be 7.5 × 10-3 kg/s. I have also computed u and it should equal T/α = 666.7 m/s. I need to solve (1) equation to find burnout velocity, then integrate it a second time to find burnout height. After that you want to basically do the same for equation (2) to get the final height. What I am most unsure about is the limits of integration I need to use.

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