Question

CSA 80kg astronaut carrying a 5kgfire extinguisher is floating inspace in the same spot. How fastwill the astronaut move if theastronaut throws the fireextinguisher with a speed of5m/s.

Answer 1

We know that the mechanical energy has to be conserved, this means that in an isoleted system we have that:

$K+U=0$

where K is the kinetic energy and U is the potential energy. Since we are in space the potential energy is zero. Then we have that:

$K=0$

Now, remember that the kinetic energy is equal to:

$\frac{1}{2}mv^2$

In this case we have that the conservation of energy means:

$\frac{1}{2}m_av^2_a=\frac{1}{2}m_bv^2_b$

Then:

$\begin{gathered} \frac{1}{2}(80)v^2_a=\frac{1}{2}(5)(5)^2 \\ v_a=\sqrt[]{\frac{5^3}{80}} \\ v_a=1.25 \end{gathered}$

Therefore the velocity of the astronaut is 1.25 m/s