Question

an 11 kg tool box is floating stationary in an orbiting spacecraft when a 79 kg astronaut, initially at rest, gives the tool box as apush. if the tool box moves with a velocity of 0.45 m/s to the left, what is the astronauts final velocity

Answer 1

The astronaut final velocity is 0.06 m/s to the right

Explanation:

In absence of external forces, the total momentum of the box-astronaut system is conserved.

At the beginnig, the total momentum of the two is zero, since they are at rest:

$p_i = 0$

While the final momentum, after the astronaut throws the box, is:

$p_f=mv+MV$

where

m = 11 kg is the mass of the box

M = 79 kg is the mass of the astronaut

v = -0.45 m/s (to the left) is the velocity of the box (we take left as negative direction)

V is the final velocity of the astronaut

The total momentum is conserved, so

$p_i = p_f\\0=mv+MV$

And solving , we find V:

$V=-\frac{mv}{M}=-\frac{(11)(-0.45)}{79}=0.06 m/s$

And the positive sign indicates that the direction is to the right.

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