A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m s - 1 . To give an initial upward acceleration of 20 m s - 2 , what is the amount of gas ejected (in kg s - 1 ) to supply the needed thrust? (Take g = 10 m s - 2 )

Step-by-step solution

Given : Mass of rocket ( m ) = 5000   Kg Exhaust speed ( v ) = 800   m   s - 1 Acceleration of rocket ( a ) = 20   m   s - 2 Gravitational acceleration ( g ) = 10   m   s - 2 We know that upward force F = m ( g + a ) = 5000 ( 10 + 20 ) = 5000 × 30 = 150000   N We also know that amount of gas ejected ( d m d t ) = F v = 150000 800 = 187.5   kg   s - 1