An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws a #8 kg# object at a speed of #3/4 m/s#, how much will his speed change by?

1 Answer
Mar 2, 2016

#v_2=8cms^-1#

Explanation:

This is a case of conservation of momentum
So, that means #m_1\vec{v_1}=m_2\vec{v_2}#

Here, subscripts of #1# refer to the object while of #2# refer to the astronaut.
So that means, #m_1=8kg# #v_1=3/2ms^-1#, #m_2=75kg#, and since the direction of movement is parallel, #\hat{v_1}=\hat{v_2}#

so, the equation reduces to #cancel{8}^2*cancel{3}^1/cancel{4}^1=cancel{75}^(25)*v_2#
So, #v_2=2/25ms^-1#

Simplification gives you that small answer up there.