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A small rocket with an initial weight of 3000 lb, including 2400 lb of fuel, is fired vertically upward. The rocket burns fuel at the rate of 40 lb/sec, which develops a thrust of, T, of 7000 lb. Considering that the drag force, D, is proportional to the square of the velocity, v, the differential equation of motion from Newton's second law is found to be(assuming the rate of mass loss is small compared to the other factors) d^2y/dt^2 + K/m(dy/dt)^2 = T/m - g OR dv/dt + K/m*v^2 = T/m - g Where m = (3000-40t)/g 0 < t ? 60 m = 600/g t > 60 T = 7000 lb 0 < t ? 60 T = 0 t > 60 Note that the mass, m, and thrust, T, vary with time as shown in figures 1 and 2. Assume that g = 32.2 ft/sec2 and is constant, and that the coefficient of aerodynamic resistance is K = 0.008 lb-sec2/ft2. Figure 1. Variation of the rocket mass in flight. Figure 2. Variation of the rocket thrust in flight. Generate a discretized version of the ODE given above using the Finite-Difference approach Solve the resulting equation to obtain the following: a. The velocity as a function of time. And Create these graphs 1) Graphs (velocity vs. time) 2) Graphs (velocity vs. height) 3) Graphs (height vs. time) 4) Graphs (acceleration vs. time) 5) Graphs (acceleration vs. height)

          A small rocket with an initial weight of 3000 lb, including 2400 lb of fuel, is fired vertically upward. The rocket burns fuel at the rate of 40 lb/sec, which develops a thrust of, T, of 7000 lb. Considering that the drag force, D, is proportional to the square of the velocity, v, the differential equation of motion from Newton's second law is found to be(assuming the rate of mass loss is small compared to the other factors)

d^2y/dt^2 + K/m(dy/dt)^2 = T/m - g

OR

dv/dt + K/m*v^2 = T/m - g

Where
m = (3000-40t)/g    0 < t ? 60
m = 600/g    t > 60

T = 7000 lb    0 < t ? 60
T = 0    t > 60

Note that the mass, m, and thrust, T, vary with time as shown in figures 1 and 2. Assume that g = 32.2 ft/sec2 and is constant, and that the coefficient of aerodynamic resistance is K = 0.008 lb-sec2/ft2.

Figure 1. Variation of the rocket mass in flight.

Figure 2. Variation of the rocket thrust in flight.

Generate a discretized version of the ODE given above using the Finite-Difference approach
Solve the resulting equation to obtain the following:
a. The velocity as a function of time. And Create these graphs
1) Graphs (velocity vs. time)
2) Graphs (velocity vs. height)
3) Graphs (height vs. time)
4) Graphs (acceleration vs. time)
5) Graphs (acceleration vs. height)

A small rocket with an initial weight of 3000 lb, including 2400 lb of fuel, is fired vertically upward. The rocket burns fuel at the rate of 40 lb/sec, which develops a thrust of, T, of 7000 lb. Considering that the drag force, D, is proportional to the square of the velocity, v, the differential equation of motion from Newton's second law is found to be(assuming the rate of mass loss is small compared to the other factors)

d^2y/dt^2 + K/m(dy/dt)^2 = T/m - g

OR

dv/dt + K/m*v^2 = T/m - g

Where
m = (3000-40t)/g 0 < t ? 60
m = 600/g t > 60

T = 7000 lb 0 < t ? 60
T = 0 t > 60

Note that the mass, m, and thrust, T, vary with time as shown in figures 1 and 2. Assume that g = 32.2 ft/sec2 and is constant, and that the coefficient of aerodynamic resistance is K = 0.008 lb-sec2/ft2.

Figure 1. Variation of the rocket mass in flight.

Figure 2. Variation of the rocket thrust in flight.

Generate a discretized version of the ODE given above using the Finite-Difference approach
Solve the resulting equation to obtain the following:
a. The velocity as a function of time. And Create these graphs
1) Graphs (velocity vs. time)
2) Graphs (velocity vs. height)
3) Graphs (height vs. time)
4) Graphs (acceleration vs. time)
5) Graphs (acceleration vs. height)

Added by Shawna M.

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