Answer:
[tex]KE2/KE1=0.71[/tex]
Explanation:
By conservation of the linear momentum:
m1*V1 = (m1+m2)*V2
Solving for V2:
[tex]V2 = \frac{m1}{m1+m2}*V1[/tex]
The kinetic energies are:
[tex]KE1=1/2*m1*V1^2[/tex]
[tex]KE2 = 1/2*(m1+m2)*V2^2[/tex]
[tex]KE2 = 1/2*(m1+m2)*(\frac{m1}{m1+m2}*V1)^2[/tex]
Simplifying:
[tex]KE2 = 1/2*\frac{m1^2}{m1+m2}*V1^2[/tex]
The ratio will be:
[tex]KE2/KE1=\frac{1/2*\frac{m1^2}{m1+m2}*V1^2}{1/2*m1*V1^2} =\frac{m1}{m1+m2}[/tex]
[tex]KE2/KE1=0.71[/tex]
