Answer:
[tex]\frac{p_{c}}{p_{b}}\approx 0.507[/tex]
Explanation:
Since the cardinal and ball have the same kinetic energy, it is possible to determine the ratio between speeds. (c for cardinal, b for baseball)
[tex]K_{c} = K_{b}[/tex]
[tex]\frac{1}{2}\cdot m_{c}\cdot v_{c}^{2}= \frac{1}{2}\cdot m_{b}\cdot v_{b}^{2}[/tex]
[tex]\frac{v_{c}}{v_{b}}=\sqrt{\frac{m_{b}}{m_{c}} }[/tex]
The ratio is obtained by multiplying each side by [tex]\frac{m_{c}}{m_{b}}[/tex]:
[tex]\frac{p_{c}}{p_{b}}=\frac{m_{c}}{m_{b}}\cdot \sqrt{\frac{m_{b}}{m_{c}} }[/tex]
[tex]\frac{p_{c}}{p_{b}}= \sqrt{\frac{m_{c}}{m_{b}} }[/tex]
The value of this ratio is:
[tex]\frac{p_{c}}{p_{b}}\approx 0.507[/tex]
