The stages of 2 stages rocket separately weigh 100 and 10 kg and contain 800 kg and 90 kg fuel respectively What is the final velocity that can be achieved with an exhaust velocity of 1.5km per sec?

Since v1 = vo + uloge(Mo/M)

For first stage ,Mo = 800+90+100+10 = 1000 kg; M = 90+10+100 = 200 kg

And vo = 0 and u = 1.5 kmsec-1

So, v1 = 0 + 1.5 loge(1000/200) = 1.5 loge 5 = 1.5 x 2.3 log10 5 = 2.415 kmsec-1

This will be the initial velocity for the second stage.

For second stage,Mo = 100kg; M = 10 kg, vo = v1 = 2.415 kmsec-1.

Thus, v2 = v1 +uloge(Mo/M)

= 2.415 + 1.5 loge 100/10 = 2.415 + 1.5 x 2.3 log10 (10) = 5.865 kmsec-1

So the final velocity achieved by the rocket = 5.865 kmsec-1