The initial velocity of the rocket, v₀ = 0

The rocket velocity after the exhaustion of the first stage is,  $\mathrm{v} = \mathrm{u} \ln \frac{{\mathrm{m}}_0}{\mathrm{m}}$​​

Here,

m₀​ = 100 + 10 + 800 + 90 = 1000 kg

and

m = 100 + 10 + 90 = 200 kg

Thus,

∣v∣ = 2ln 5 = 2×1.609 = 3.281 km/s

The second stage becomes operative when the first is detached from it.

Thus,

u₀​ = 3.218 km/s

m₀ ​= 10 + 90 = 100kg

m = 10kg

Thus

∣v∣ = 3.22 + 2ln $\frac{100}{10}$

= 3.22 + 2×(2.3) = 7.82 km/s = 7.8×10³ m/s