Answer: Vce= 4234.4km/hr or 1180m/s
Explanation:
Mass of rocket motor Mr= 4m
Mass of control module Mc= m
Initial velocity of spaceship relative to earth Vs= 4300km/hr
Final velocity of command module relative to the rocket motor Vrc = 82km/hr
Total mass of spaceship M= 4m+m= 5m
Using law of conservation of momentum;
MVs= MrVre + McVce eqn1
Vre = Vrc+Vce eqn2
Where Vce is velocity of control room relative to the earth and Vre is velocity of rocket motor relative to the earth
Substituting eqn2 to eqn1, we have.
MVs= Mr(Vrc+Vce) +McVce
MVs= MrVrc+MrVce+McVce
Making Vce the subject of formula.
Vce = (MVs-MrVrc)/(Mc+Mr)
Substituting the values we have,
Vce = (5m×4300km/hr - 4m×82km/hr)/ (m+4m)
Vce = 21172m/5m
Vce= 4234.4km/hr or 1180m/s
