Solve in MATLAB
Problem 2: Rocket Motion The ideal motion of a simple single-stage rocket can be modeled as follows When thrust is being produced, the velocity of the rocket after it is launched from a stationary position is given by m(t) where Isp is the specific impulse in seconds (a function of the chemical propellant type), g is the gravitational constant, mo is the initial mass of the rocket (structure and fuel) and m(t) is the mass of the rocket at time t. The mass of the rocket at time t can be determined based on the rate at which the fuel is burned (b, in units of mass/second) m(t) = mo-bt. Once all of the fuel is burned, the rocket acts as a simple projectile (v- vo- gt) Table 1 gives the parameters for the problem. Use these parameters and the equations above to calculate and plot the mass, velocity, and height of the rocket as a function of time. Also print the burn time (occurs at maximum velocity) Total Mass (Rocket Mass of Fuel Burn Rate Fuel 0.4 k 35.8 12.78 g/s 200 s Table 1: Model rocket parameters Before beginning to write your script program, produce pseudocode for the problem. You will need to submit your pseudocode in addition to your MATLAB code. Hints 1.) Choose a time increment At of.001 s 2.) Create vectors of mass, velocity, and height as you increment time. Use the same index variable for all of these 3.) Use a while-loop to indicate that while there is still fuel, Eq. 1 should be used. Within that loop, increase your index variable, and calculate mass, time, velocity, and height. These will be discretized based on the time increment. 4.) Use a second while-loop to calculate these quantities after fuel is expired. 5.) Use the "subplot" function to create the 3x1 plot. Note: There are many ways to do this problem. It is recommended that you use while-loops here specifically for practice Problem 2: Rocket Motion The ideal motion of a simple single-stage rocket can be modeled as follows When thrust is being produced, the velocity of the rocket after it is launched from a stationary position is given by m(t) where Isp is the specific impulse in seconds (a function of the chemical propellant type), g is the gravitational constant, mo is the initial mass of the rocket (structure and fuel) and m(t) is the mass of the rocket at time t. The mass of the rocket at time t can be determined based on the rate at which the fuel is burned (b, in units of mass/second) m(t) = mo-bt. Once all of the fuel is burned, the rocket acts as a simple projectile (v- vo- gt) Table 1 gives the parameters for the problem. Use these parameters and the equations above to calculate and plot the mass, velocity, and height of the rocket as a function of time. Also print the burn time (occurs at maximum velocity) Total Mass (Rocket Mass of Fuel Burn Rate Fuel 0.4 k 35.8 12.78 g/s 200 s Table 1: Model rocket parameters Before beginning to write your script program, produce pseudocode for the problem. You will need to submit your pseudocode in addition to your MATLAB code. Hints 1.) Choose a time increment At of.001 s 2.) Create vectors of mass, velocity, and height as you increment time. Use the same index variable for all of these 3.) Use a while-loop to indicate that while there is still fuel, Eq. 1 should be used. Within that loop, increase your index variable, and calculate mass, time, velocity, and height. These will be discretized based on the time increment. 4.) Use a second while-loop to calculate these quantities after fuel is expired. 5.) Use the "subplot" function to create the 3x1 plot. Note: There are many ways to do this problem. It is recommended that you use while-loops here specifically for practice
