Question

For a rocket moving in free space, the fraction of mass to be disposed of Off to attain a speed equal to two times the exhaust speed is given by (given e? = 7.4)

1.0.40

2. 0.37

3. 0.50

4. 0.86​

Answer 1

4. 0.86​

Explanation:

Given: e^2 = 7.4 and attain a speed equal to two times the exhaust speed.

Solution:

The relationship between the velocity of the rocket at any time t and its mass is m is as follows:

 v = u log(mo/md)

 [mo/(mo- md)] =  e^(v/u)

where md is the disposed mass and mo is the initial mass of the rocket.

Now, it is given that the rocket needs to attain twice the exhaust speed, meaning (v/u) = 2.

So the fraction of mass to be disposed off (md/mo) to attain a speed equal to two times the exhaust speed can be calculated as follows:

  mo/(mo- md) =  e^(v/u) = 7.4

  mo/(mo- md) =  7.4

   mo = 7.4mo - 7.4md

  7.4md = 6.4mo

  So md/mo = 6.4 / 7.4 = 0.86

Option 4 is the answer.