We have two events that occurred on different axes, the most convenient is to perform the operations on the two axes, and then look for the resulting force.
Our values are,
[tex]m_1=1kg\\m_2 = 2kg\\v_1' = 1.2m/s\\v_1''= 0.8m/s[/tex]
PAR A) For the X axis, we apply momentum conservation, which is given by,
Total momentum before = Total momentum After
We start from rest, so in X the initial speeds are 0,
[tex]m_1v_1+m_2v_2=m_1v_1'+m_2v_2'[/tex]
[tex]0+0 = (1*1.2)+(1)v_2'[/tex]
[tex]V_2' = -1.2m/s[/tex]
Now we apply for the conservation of the moment, it is part of the rest, so,
[tex]m_1v_1+m_2v_2=m_1v_1''+m_2v_2''[/tex]
[tex]0+0=2*0.8+1*v_2''[/tex]
[tex]v_2'' = -1.6[/tex]
To find the total speed, we simply apply pitagoras,
[tex]V = \sqrt{v_2'^2+v_2^2''}[/tex]
[tex]V = \sqrt{1.2^2+1.6^2}[/tex]
[tex]V = 2m/s[/tex]
PART B) The address is given by,
[tex]tan\theta = \frac{V_2''}{V_2'}[/tex]
[tex]\theta = tan^{-1} \frac{V_2''}{V_2'}[/tex]
[tex]\theta = tan^{-1} \frac{1.6}{1.2}[/tex]
[tex]\theta = 53.31\° [/tex] (Below -x axis)
