A spaceship moving at 1000m/s releases a satellite of Mass 1000kg at a speed of 1000m/s. What is the mass of the spaceship if it slows down to a velocity of 910m/s? show all steps of solve
In this problem, we are dealing with a conservation of linear momentum. The linear momentum before the satellite is released is equal to the linear momentum after the satellite is released. Let the mass of the spaceship be m.
Initially, we only have the linear momentum of the spaceship (since the satellite's velocity is 0 at the moment it is released). So the initial momentum is given by:
Initial momentum = m × 1000m/s
Once the satellite is released, both the spaceship and the satellite will have linear momentum. The problem tells us that the satellite is released at a speed of 1000m/s and that the spaceship slows down to 910m/s. So the final momentum would be:
Final momentum = (m × 910m/s) + (1000kg × 1000m/s)
Now, we can use the conservation of linear momentum equation:
Initial momentum = Final momentum
m × 1000m/s = (m × 910m/s) + (1000kg × 1000m/s)
1000m = 910m + 1000000
Rearrange to solve for the mass of the spaceship, m:
90m = 1000000
m = 1000000 ÷ 90
m ≈ 11111.1 kg
The mass of the spaceship is approximately 11,111.1 kg.