Initial velocity of the rocket, v = 2 km/s = 2 × 10³ m/s
Mass of Mars, M = 6.4 × 10²³ kg
Radius of Mars, R = 3395 km = 3.395 × 10⁶ m
Universal gravitational constant, G = 6.67× 10^–11 N m² kg^–2
Mass of the rocket = m
Initial kinetic energy of the rocket = (1/2)mv²
Initial potential energy of the rocket = -GMm / R
Total initial energy = (1/2)mv²- GMm / R
If 20 % of initial kinetic energy is lost due to Martian atmospheric resistance, then only 80 % of its kinetic energy helps in reaching a height.
Total initial energy available = (80/100) × (1/2) mv² - GMm / R  =  0.4mv² - GMm / R
Maximum height reached by the rocket = h
At this height, the velocity and hence, the kinetic energy of the rocket will become zero.
Total energy of the rocket at height h = -GMm / (R + h)

Applying the law of conservation of energy for the rocket, we can write: 
0.4mv² - GMm / R  =  -GMm / (R + h)
0.4v² = GM / R  -  GM / (R + h)
= GMh / R(R + h)
(R + h) / h  =  GM / 0.4v²R
R / h  =  ( GM / 0.4v²R )  -  1
h = R / [ (GM / 0.4v²R) - 1 ]
= 0.4R²v² / (GM - 0.4v²R)
= 0.4 × (3.395 × 10⁶)² × (2 × 10³)² / [ 6.67 × 10^-11 × 6.4 × 10²³  -  0.4 × (2 × 10³)² × (3.395 × 10⁶) ]
= 18.442 × 10¹⁸ / [ 42.688 × 10¹²  -  5.432 × 10¹² ]
= 18.442 × 10⁶ / 37.256
= 495 × 10³ m = 495 km.