(Solved): Problem 4 The burnout velocity for a N-stage rocket in the restricted limit c ...

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Problem 4 The burnout velocity for a $$\mathrm{N}$$-stage rocket in the restricted limit can be calculated via the equation: $$v_{b_{N?stage}}=I_{sp}{g}_0\ln \left({\left[\frac{1}{{?}_{PL}^{1/N}(1??)+?}\right]}^N\right)$$ a) Write a MATLAB function for evaluate the burnout speed for a rocket with the following parameters: the specific impulse $$I_{sp}=316\mathrm{s}$$, the structural ratio $$?=0.10$$, the payload fraction $${?}_{PL}=0.05$$. Numerically deduce (i.e. use the for loop or the while loop) the number of rocket stages needed to attain a 1st cosmic velocity, i.e. $$7.9\mathrm{km}/\mathrm{s}$$, for the parameters given. b) Numerically deduce (i.e. use the for or the while loop) the number of rocket stages needed to attain a burnout velocity that is $$98\%$$ of that generated for an infinite number of stages, i.e. $$8.444\mathrm{km}/\mathrm{s}$$, for the parameters given. c) Plot burnout velocity as a function of the number of rocket stages $$N$$. Hint: you can use the Matlab function stairs () to plot is.