NASA is designing a Mars-lander that will enter the Martian atmosphere at high speed. To land safely it must slow to a constant vertical speed of 20 m/s after deploying a parachute with an area of 200 m^2. The drag coefficient of the parachute is 1.855. The acceleration due to gravity on Mars is 3.71 m/s2, and the density of the atmosphere near the surface is 0.01 kg/m^3.
a. Calculate the maximum mass of the Mars lander to ensure it can land safely?
b. The mission designers consider a larger lander with a mass of 480 kg. Show that the parachute required would be larger than 400 m².
c. To test the lander before launching it to Mars, it is tested on Earth where g = 9.8 m/s^2 and the atmospheric density is 1.0 kg m-3. How big should the parachute be for the terminal speed to be 20 m/s, if the mass of the lander is 480 kg?
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