Answer:
[tex]p=21.24\ kg\ m/s[/tex]
[tex]\theta=39.46^{\circ}[/tex] over the x axis.
Explanation:
We have to add their linear momentum as a vector.
For piece 1:
[tex]p_1=m_1v_1=(0.2kg)(82m/s)=16.4\ kg\ m/s[/tex] along the x axis.
For piece 2:
[tex]p_2=m_2v_2=(0.3kg)(45m/s)=13.5\ kg\ m/s[/tex] along the y axis.
Since both are perpendicular, we get the the magnitude of the vectorial sum of them with:
[tex]p=\sqrt{p_1^2+p_2^2}=\sqrt{(16.4\ kg\ m/s)^2+(13.5\ kg\ m/s)^2}=21.24\ kg\ m/s[/tex]
And the angle over the x axis can be calculated as:
[tex]\theta=arctan(\frac{13.5}{16.4})=39.46^{\circ}[/tex]
