Question

A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 minute after the blast is

Answer 1

Thrust = -uR (R is rate of mass ejection) 

u is exhaust velocity relative to the rocket 

since the gas is travelling at 12000 m/s relative to the rocket 

u = - 12000 (opp direction of rocket motion) 

after 1 minute mass of rocket = 5700 - 15x60 = 4800 kg 

Thrust = -uR = -(-12000)15 = 180000 N (in the direction of rocket motion) 

Thrust - 4800g = 4800a 

=> 180000 - 4800x10 = 4800a 

=> 132000 = 4800a 

=> a = 132000 / 4800 = 27.5 m/s² 

Ans: acceleration of rocket = 27.5 m/s² 

b) Thrust = -uR -------------------------------> (i) 

=> Thrust required for initial upward acceleration of 20m/s² 

= 5000g + 5000(20) -------------------------> [Fresultant = ma, thrust - w = ma] 

= 50000 + 100000 = 150000 N 


from (i) => R = -Th./u = -150000/-800 

= 1500/8 = 187.5 kg/s
answer is 187.5
Hope this helps you