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if the two stages of a rocket weights 100kg and 10 kg separately and contain 800kg and 90kg fuel separately what is the final velocity that can be achieved with an exhaust velocity of 1.5km/sec

if the two stages of a  rocket weights 100kg and 10 kg separately and  contain 800kg and 90kg fuel separately what is the final velocity that can be  achieved with an exhaust velocity of 1.5km/sec

Grade:12th pass

1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
The initial velocity of the rocket V0 = 0

Velocity of the rocket after exhaustion of the forst stage is

V = μ ln m0 / m

Here,

m0 = 100 + 10 + 800 +90 = 1000 kg

m = 100 + 10 + 90 = 200 Kg

Thus |V| = 2 ln 5

= 2 x 1.609

= 3.218 Km/s

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

μ0 = 3.218 Km/s

m0 = 10 + 90 = 100 Kg

m = 10 Kg

Thus, |V| = 3.22 + 2ln (100 /10)

= 3.22 + 2 X (2.3)

= 7.82 X 10^3 m/s

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