With the engines off, a spaceship is coasting at avelocity of +260m/s through outer space. The ship carries rockets that are mounted in firing tubes, the back ends of which are closed. It fires a rocket straight ahead at an enemy vessel. The mass of the rocket is 1100kg, and the mass of the spaceship (not including the rocket) is 5000000kg. The firing of the rocket brings the spaceship to a halt. What is the velocity of the rocket?
Momentum is conserved.
MassRocket*changevelocityrocket=massShip(changevelocity sship)
Now the change in rocket velocity is (Vr-260m/s). The change in ship velocity is -260m/s
solve for velocity of the rocket.
To solve for the velocity of the rocket, we need to use the principle of conservation of momentum. This principle states that the total momentum of a system of objects remains constant if no external forces act on the system.
In this scenario, before the rocket is fired, the momentum of the system consisting of the rocket and the spaceship is zero, since the spaceship is coasting at a velocity of +260m/s and there are no external forces acting on the system.
After firing the rocket, the momentum of the rocket and the spaceship must still be zero, as there are no external forces to change the momentum of the system. This means that the change in momentum of the spaceship must be equal in magnitude and opposite in direction to the change in momentum of the rocket.
Using the principle of conservation of momentum, we can set up an equation:
Mass of the rocket * Change in velocity of the rocket = Mass of the spaceship * Change in velocity of the spaceship
Substituting in the given values:
(1100kg) * (Vr - 260m/s) = (5000000kg) * (-260m/s)
Now we can solve for the velocity of the rocket, Vr:
1100kg * Vr - 286000kgm/s = -1300000000kgm/s
1100kg * Vr = -1300000000kgm/s + 286000kgm/s
1100kg * Vr = -1299714000kgm/s
Vr = (-1299714000kgm/s) / (1100kg)
Vr ≈ -1181558.2 m/s
The velocity of the rocket, taking into account the direction, is approximately -1181558.2 m/s.