Abody of mass 4.5 kg makes an elastic collision with another body at rest and continues to move in the original direction but with 1/5 of its original speed. (a) what is the mass of the other body? (b) what is the speed of the two-body center of mass if the initial speed of the 4.5 kg body was 8.9 m/s?

Answer with Explanation:

We are given that

Mass of one body=4.5 kg

Initial velocity of one body=8.9 m/s

Initial velocity of another body=0

Final velocity of one body=

a.We have to find the mass of the other body.

Energy and momentum are conserved in this system

 (equation I)

From conservation of kinetic energy

(equation II)

Substitute equation I in equation II

Substitute the given values then we get

Hence, the mass of other body=3 kg

b.We have to find the speed of two body center of mass .

The center of mass speed  is given by

Substitute the values then we get

Hence, the speed of the two body center of mass is given by =5.34 m/s