A rocket is fired vertically from the surface of mars with a speed of 2 km/s. If 20% of its initial energy is lost due to martian atmosphere resistance how far (in km) will the rocket go from the surface of mars before returning to it? Mass of mars `=6.4xx10^(23)` kg, radius of mars =3395 km, `G=6.67xx10^(-11)Nm^(2)//kg^(2)`.

Explanation

To solve the problem step by step, we need to calculate how far the rocket will go before returning to the surface of Mars, taking into account the energy loss due to atmospheric resistance.

### Step 1: Calculate the Initial Kinetic Energy
The initial kinetic energy (KE_initial) of the rocket can be calculated using the formula:
\[ KE_{\text{initial}} = \frac{1}{2} mv^2 \]
where:
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