A rocket lifts off from Earth initially at a mass of 50,000 kg. If it burns 40,000 kg offuel during 40 seconds, it increases its speed by 5 km/s.1. What is the exhaust velocity of the rocket?2. What is the mass loss rate of the rocket?3. What is the thrust of the rocket?

Name: A rocket lifts off from Earth initially at a mass of 50,000 kg. If it
Uploaded: 2024-03-20T06:56:55.000Z
Channel: Bartleby
Description: A rocket lifts off from Earth initially at a mass of 50,000 kg. If it burns 40,000 kg offuel during 40 seconds, it increases its speed by 5 km/s.1. What is the exhaust velocity of the rocket?2. What is the mass loss rate of the rocket?3. What is the

Given:initial mass of the rocket, mi=50000 kgfuel burns, mf=40000 kgrate of fuel burns, dmdt=4000040=1000 kg/ssuppose intial speed of rocket=u m/sincrease in speed=5 km/s or 5000 m/sFinal speed of rocket, vf=u+5000Using newton's 1st equation of motion,vf=u+at,within 40 s the acceleration of rocket is a,vf-u=a×40vf-u=5000 m/sa×40=5000,a=125 m/s2,initial velocity of rocket while launching is u,Applying rocket propulsion equation,ma=Ft-mg,Ft=thrust force=udmdt,ma=udmdt-mg,50000×125=u×1000-50000×9.81,u=6740.5 m/s,Exhaust velocity of the rocket is 6740.5 m/s,Part 2:mass loss rate of the rocket, dmdt=1000 kg/sPart 3:Thrust of the rocket,Ft=udmdt=6740.5×1000Ft=6740500 N