Answer :
Answer:
The mass of the other body is 2.57 kg.
Explanation:
The expression of the velocity of an object in an elastic collision is as follows;
[tex]v_1=(\frac{m_1-m_2}{m_1+m_2})u_1+(\frac{2m_2}{m_1+m_2})u_2[/tex]
Here, [tex]m_1[/tex],[tex]m_2[/tex] are the masses of the objects, [tex]u_1[/tex],[tex]u_2[/tex] are the initial speed of the objects and [tex]v_1[/tex] is the final speed.
According to the given problem, a body of mass 3.6 kg makes an elastic collision with another body at rest and continues to move in the original direction but with 1/6 of its original speed.
[tex]v_1=\frac{1}{6}u_1[/tex]
Calculate the mass, [tex]m_2[/tex].
[tex]v_1=(\frac{m_1-m_2}{m_1+m_2})u_1+(\frac{2m_2}{m_1+m_2})u_2[/tex]
Put [tex]v_1=\frac{1}{6}u_1[/tex], [tex]u_2=0[/tex] and [tex]m_1=3.6 kg[/tex].
[tex]\frac{1}{6}u_1=(\frac{m_1-m_2}{m_1+m_2})u_1+(\frac{2m_2}{m_1+m_2})(0)[/tex]
[tex]\frac{1}{6}u_1=(\frac{m_1-m_2}{m_1+m_2})u_1[/tex]
[tex]\frac{1}{6}=(\frac{3.6-m_2}{3.6+m_2})[/tex]
[tex]m_2=2.57 kg[/tex]
Therefore, the mass of the other body is 2.57 kg.