Question

Two astronauts, one of mass 64 kgkg and the other 86 kgkg , are initially at rest together in outer space. They then push each other apart. Part A How far apart are they when the lighter astronaut has moved 10 mm

Answer 1

Given :

Two astronauts, one of mass 64 kg and the other 86 kg , are initially at rest together in outer space.

To Find :

How far apart are they when the lighter astronaut has moved 10 mm.

Solution :

Since, there is no force in space.

So, applying conservation of momentum :

$64v_1 + 86v_2 = 0\\\\v_2 = - \dfrac{32}{43}v_2$

We know, distance travelled by smaller astronaut is :

$10 = v_1t$

For bigger astronaut distance travelled :

$v_2t = -\dfrac{32}{43}(v_1t)\\\\v_2t = -\dfrac{32}{43}\times 10\\\\v_2t = -7.44\ mm$

Therefore, they are ( 10 + 7.44 ) = 17.44 mm apart from each others.

Hence, this is the required solution.