The Mars Curiosity rover was required to land on the surface of Mars with a velocity of 1 m/s. Given the mass of the landing vehicle and parachute is 2270 kg, the drag coefficient is effectively 0.5, the atmosphere density is 0.71 that of Earth (take Earth atmosphere density as 1.2 kg/m3), and the Martian gravitational acceleration is 3.689 m/s2, find the required total frontal area (in m2) of the lander plus a parachute to land at the given velocity. Assume the landing vehicle has achieved terminal velocity as it falls through the Martian atmosphere.

The value is      

Explanation:

From the question we are told that

    The velocity which the rover is suppose to land with is  

    The  mass of the rover and the parachute is  

     The  drag coefficient is  

      The atmospheric density of Earth  is  

     The acceleration due to gravity in Mars is  

Generally the Mars  atmosphere density is mathematically represented as

=>        

=>        

Generally the drag force on the rover and the parachute  is mathematically represented as

=>        

=>        

Gnerally this drag force is mathematically represented as

Here A is the frontal area

So  

=>      

=>      

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