The curved-earth gravity-turn equations for a rocket with thrust vectoring (for Question 3): dtdv=mTcosDgsindtd=(RE+hvvg)cosmvTsindtdh=vsindtdx=RE+hREvcosg(h)=(1+REh)2g0;D(v,h)=CDAq;q=21v2;(h)=0ehAhRE=6378km;g0=9.81m/s2;0=1.225kg/m3;hA=7.5km. Here is the angle between the vector of thrust and the vector of velocity. Earth's gravitational parameter, =398,600km3s2 Problem 4 The burnout velocity for a N-stage rocket in the restricted limit can be calculated via the equation: vbNstage=Ispg0ln([PL1/N(1)+1]N) a) Write a MATLAB function for evaluate the burnout speed for a rocket with the following parameters: the specific impulse Isp=316s, 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. 7.9km/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. 8.444km/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