Abody of mass 2.7 kg makes an elastic collision with another body at rest and continues to move in the original direction but with 1/3 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 id the initial speed of the 2.7kg body was 4.0 m/s?

a)

1.35 kg

b)

2.67 ms⁻¹

Explanation:

a)

= mass of first body = 2.7 kg

= mass of second body = ?

= initial velocity of the first body before collision =

= initial velocity of the second body before collision = 0 m/s

= final velocity of the first body after collision =

using conservation of momentum equation

Using conservation of kinetic energy

b)

= mass of first body = 2.7 kg

= mass of second body = 1.35 kg

= initial velocity of the first body before collision = 4 ms⁻¹

= initial velocity of the second body before collision = 0 m/s

Speed of the center of mass of two-body system is given as

ms⁻¹