A test rocket is launched (zero initial velocity) in the desert at an initial height of 832 meters above sea level. The initial mass is 3380 kilograms and the final mass, after the solid fuel is burned, is 2440 kg. The rocket engine will burn for about 10.3 seconds. At the initial altitude above sea-level, the thrust of the engine is 153,510 Newtons. Assume a coefficient of $k = 0.43$ for drag.
Use Euler's method, with step size of 0.5 seconds, to compute the velocity of the rocket over time. Create a table listing the time (in seconds) and the velocity (in m/s) for the first 10.5 seconds of the launch. Copy the table below or attach. Label the values in the table.
Find a linear regression model for the velocity and write the resulting velocity as a function of time below.
What is the average acceleration experienced by the rocket during the first 10 seconds of flight? What does this mean in terms of the g-force experienced by an astronaut on the rocket?
Assuming the initial height of $h_0 = 832$ meters, integrate the velocity function to find a function for height during the launch. Write the height function below. What does the model predict as the height at 10 seconds and at 11 seconds?
