Calculate the ration `m _(0)//m` for a rocket if it is to escape from the earth . Given escape velocity `= 11.2 km//s ` and exhaust speed of gases is `2 km// s` .

Explanation

Assuming that the rocket starts from rest, velocity acquired is given by
` upsilon = u log_(e) ((m_(0))/(m)) = 2.3026u log_(10) (m_(0)/(m)) `
Now , ` upsilon = 11.2 km//s ` and ` u=2 km//s `
` :.` `11.2 = 2. 3026 xx 2 log_(10)(m_(0)/(m)) `
`log_(10) (m_(0)/(m)) = (11.2)/(2.23026 xx2) = 2.432 `
` m_(0)/(m) = "antilog" 2.432 = 270.4 ` .