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EXERCISE 1 – Rocket in the Absence of Outside Forces A V2 rocket has an empty mass of 4000kg and was loaded with 8800kg of fuel. It burned fuel at 129.4kg/s and had an exhaust velocity of 2050m/s. Use the last two pieces of information to calculate an effective thrust, and use the Euler-Cromer method to solve for the velocity of the rocket in one dimension in the absence of gravity, noting that it will be changing its mass at each step. Compare the computed velocity at each time to the results predicted by the Rocket Equation.

EXERCISE 2 – Rocket in a Constant Gravitational Field Modify the model from Exercise 1 by adding in a constant gravity. Note that while g will not change with time, the weight will. Write code so that when the rocket runs out of fuel, its mass stops changing, and the thrust goes to zero. Graph the resulting 1-D position, velocity and acceleration as a function of time and comment.

Exercise 3 - Rocket in a Newtonian Gravitational Field Modify the results from Exercise 2 to account for the weakening of gravity as a function of distance from the center of the Earth. Graph the resulting 1-D position and velocity as a function of time.

Exercise 4 – Drag on a Rocket with Constant Air Density Using the results of either Exercise 2 or 3, add in the effects of drag. Assume that a V2 has a diameter of 1.65m, a drag coefficient of 0.125 and that the density of air is 1.22kg/m^3. Graph the resulting 1-D position and velocity as a function of time. Calculate a maximum height and compare that result to previous numbers

Exercise 1 - Rocket in the Absence of Outside Forces: To calculate the effective thrust, we can use the formula: Thrust = (burn rate of fuel) * (exhaust velocity) Given:

Empty mass ( ) = 4000 kg Fuel mass ( ) = 8800 kg Burn rate of fuel = 129.4 kg/s Exhaust velocity = 2050 m/s Thrust = Thrust = Now, let's use the Euler-Cromer method to solve for the velocity of the rocket in one dimension in the absence of gravity. We'll assume a small time step, ?t, for the calculations. Let's denote: v(t) = velocity of the rocket at time t m(t) = mass of the rocket at time t We can use the following equations of motion: