Question

An astronaut with a mass of `75` `kg` is floating in space. If the astronaut throws an object with a mass of `17` `kg` at a speed of `5/6` `ms^-1`, how much will his speed change by?

Answer 1

The speed of the astronaut will change by `0.18` `ms^-1` in a direction opposite to the direction in which the object was thrown.

Explanation:

Momentum is conserved: the total momentum before the throw is the same as the total momentum after.

Motion is relative, but in the frame of reference of the astronaut, assumed he is stationary, and the object is stationary with him. That means the overall momentum before the throw is `0` `kgms^-1`.

The momentum of the thrown object is given by:

`p=mv=17*5/6=14.2` `kgms^-1`

The momentum of the astronaut will have the same magnitude and be in the opposite direction. This is related to Newton's Third Law .

Rearranging the momentum equation to make velocity the subject:

`v=p/m`

Substituting in the momentum of the object and the mass of the astronaut:

`v=p/m = 14.2/75 = 0.18` `ms^-1` in the opposite direction to the motion of the object.

It makes sense that the velocity of the astronaut is much smaller than the velocity of the object, since his mass is much larger.