Explanation:
It is given that,
Mass of cardinal,[tex]m_c=4.2\times 10^{-2}\ kg[/tex]
Mass of baseball, [tex]m_b=0.146\ kg[/tex]
Both cardinal and baseball have same kinetic energy. We need to find the ratio of the cardinal's magnitude [tex]p_c[/tex] of momentum to the magnitude [tex]p_c[/tex] of the baseball's momentum.
[tex]E_c=E_b[/tex]
Kinetic energy is given by, [tex]E=\dfrac{p^2}{2m}[/tex]
[tex]\dfrac{p_c^2}{2m_c}=\dfrac{p_b^2}{2m_b}[/tex]
[tex](\dfrac{p_c}{p_b})^2=\dfrac{m_c}{m_b}[/tex]
[tex]\dfrac{p_c}{p_b}=\sqrt{\dfrac{m_c}{m_b}}[/tex]
[tex]\dfrac{p_c}{p_b}=\sqrt{\dfrac{4.2\times 10^{-2}}{0.146}}[/tex]
So, [tex]\dfrac{p_c}{p_b}=\dfrac{53}{100}[/tex]
So, the ratio of cardinal's magnitude of momentum to the magnitude of the baseball's momentum is 53 : 100
