Conservation of Momentum homework help

[court2011]

Homework Statement

A 93 kg astronaut and a 1500 kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.16 m/s directly away from the shuttle. Seven-and-a-half seconds later the astronaut comes into contact with the shuttle. What was the initial distance from the shuttle to the astronaut?

Homework Equations

$$\sum$$F= $$\Delta$$p/$$\Delta$$t

The Attempt at a Solution

 

[XanziBar]

You can use the conservation of momentum Pi=Pf when there are no external forces to find the velocity of the astronaut. Then use speed=distance/time to find the distance.

 

[kerimek]

To solve this problem, we can use the conservation of momentum principle, which states that the total momentum of a system remains constant if there is no external force acting on the system. In this case, the system consists of the astronaut, satellite, and shuttle. Initially, the total momentum of the system is zero since all three objects are at rest. After the astronaut pushes the satellite, the total momentum remains zero, but the satellite now has a momentum of 240 kg m/s (calculated by multiplying its mass of 1500 kg by its velocity of 0.16 m/s).

Using the conservation of momentum equation, we can set the initial momentum of the system equal to the final momentum:
0 = 240 kg m/s + ma, where ma is the momentum of the astronaut after coming into contact with the shuttle.

Since the astronaut and shuttle are now in contact, they will have the same velocity. We can use the fact that the astronaut and shuttle have the same mass to set up another equation:
ma(0.16 m/s) = (93 kg + ma)(0.16 m/s)

Solving for ma, we get a value of 93 kg for the momentum of the astronaut.

Now, we can use this value to solve for the initial distance between the astronaut and the shuttle. We can use the equation for distance, d = v0t + (1/2)at^2, where v0 is the initial velocity, t is the time, and a is the acceleration. Since we know the initial velocity and time, we can solve for the initial distance:
d = (0.16 m/s)(7.5 s) + (1/2)(0)(7.5 s)^2 = 0.6 m

Therefore, the initial distance between the astronaut and the shuttle was 0.6 meters.