Conservation of momentum problem regarding a missing mass of a ship

[MichaelDunlevy]

Homework Statement

After a malfunction, an astronaut escapes from a doomed spacecraft by using an escape pod that is blown off of the ship. The small explosion sends the pod flying away at 34.9 m/s, while the main ship moves in the opposite direction at the speed of 1.89 cm/s. If the combined mass of the astronaut and pod is 1270 kg, what is the mass of the doomed spacecraft ?

Homework Equations

Conservation of Momentum:

m1u1+m2u2 (initial) = m1v1+m2v2 (final)

The Attempt at a Solution

I believe that conservation of momentum is the correct principle to use here, but I am unsure how to solve for the spaceship's mass because of the missing initial velocity. Could someone help me out? Thanks!

 

[Bandersnatch]

Hi there!

The initial velocity was meant to be 0 for both the ship and the pod.
Those velocities provided are for after the separation, relative to their mutual centre of mass.

 

[Siune]

If the spaceship and pod before the launch had 0 momentum to their mutual centre of mass, the conservation of momentum says:

the pod and spaceship must have right after the launch 0 momentum to their mutual centre of mass. So you have 4 variables ( as intial velocities were both 0 ) after the launch; ( mass and velocity of spaceship and pod ).

 

[MichaelDunlevy]

thank you! i figured that the velocity must have been an unknown constant (which would be ridiculous) or 0. I just wanted verification. Thank you for the fast reply guys!

 

[Nickie]

You are correct in using conservation of momentum to solve this problem. In order to solve for the mass of the spaceship, you will need to use the equation m1u1+m2u2 = m1v1+m2v2, where m1 and u1 represent the mass and initial velocity of the astronaut and pod, and m2 and u2 represent the mass and initial velocity of the spaceship. Since the initial velocity of the spaceship is missing, we can use the fact that the total momentum before and after the explosion must be equal, and set the initial momentum (m1u1+m2u2) equal to the final momentum (m1v1+m2v2). This will allow us to solve for the missing mass of the spaceship. So, we have:

m1u1+m2u2 = m1v1+m2v2
(1270 kg)(34.9 m/s) + m2(1.89 cm/s) = (1270 kg)(0 m/s) + m2(0 m/s)
44273 kg*m/s + 0.0189 m2/s = 0 kg*m/s + 0 kg*m/s
44273 kg*m/s = 0.0189 m2/s

Solving for m2, we get:

m2 = (44273 kg*m/s) / (0.0189 m/s)
m2 = 2.34 x 10^6 kg

Therefore, the mass of the spaceship is approximately 2.34 x 10^6 kg.