Question

Two astronauts are 137m away from their spacecraft and both are untethered. The larger one of mass “m” (including the mass of the spacesuit etc.) has plenty of oxygen while his partner is running low.

1. How hard must he push her if she has a mas of “m” so that she can make it back to spacecraft in time to be rescued if her oxygen will only last 2 more minutes?

2. How far away from the spacecraft will he be when she collides with it?

Answer 1

Given:

distance of astronauts from the spacecraft,

mass of the heavier astronaut having enough oxygen,

mass of the astronaut with scarce oxygen,

initial velocity of the heavier astronaut,

initial velocity of the lighter astronaut,

Now, using the conservation of linear momentum:

Net initial momentum = Net Final momentum

since the two bodies are initially at rest

....................................(1)

Negative sign just denotes that the two velocities are in opposite direction.

1)

Given that we have a times span of 120 seconds (2 minutes) for the lighter astronaut to get to the spacecraft safely.

Using equation of motion:

Force required to generate this acceleration:

2) Distance travelled by the heavier astronaut after the end of the given can be calculated as:

So, its distcance from the spacecraft is: