A space vehicle is traveling at 4980 km/h relative to Earth when the exhausted r

Question

A space vehicle is traveling at 4980 km/h relative to Earth when the exhausted rocket motor is disengaged and sent backward. The relative speed between the motor and the command module is then 84 km/h. The mass of the motor is four times the mass of the module. What is the speed of the command module relative to Earth just after the separation? A space vehicle is traveling at 4980 km/h relative to Earth when the exhausted rocket motor is disengaged and sent backward. The relative speed between the motor and the command module is then 84 km/h. The mass of the motor is four times the mass of the module. What is the speed of the command module relative to Earth just after the separation?

Explanation / Answer

given

initial velocity u = 4980 km / h

the velocity of the motor is Vb - Va = 84 km / h

then Va = Vb - 84

say the mass of command module is = m and

mass of the motor is = 4 m

then the mass of the vehicle before disengaged is = m + 4 m = 5 m

using the law of conservation of momentum is

( 5 m ) X u = 4 m X Va + m X Vb

5 X m X u = 4 m X ( Vb - 84 )+ m X Vb

5 X u = 4 ( Vb - 84 )+ Vb

5 X 4980 = 4 ( Vb - 84 )+ Vb

24900 = 4 Vb - 336 + Vb   

5 Vb = 24900 - 336

Vb = 24564 / 5

Vb = 4912.8 km/h

the speed of the command module relative to Earth

just after the separation Vb = 4912.8 km/h

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.