A closed system consists of two particles of masses `m_1` and `m_2` which move at right angles to each other with velocities `v_1` and `v_2`. Find:
(a) the momentum of each particle and
(b) the total kinetic energy of the two particles in the reference frame fixed to their centre of inertia.

Explanation

(a) Let the particles `m_1` and `m_2` moves with velocities `vecv_1` and `vecv_2` respectively.
`overset~p=mu v_(rel)=mu|vecv_1-vecv_2|`
As `vecv_1_|_vecv_2`
So, `overset~p=musqrt(v_1^2+v_2^2)` where `mu=(m_1m_2)/(m_1+m_2)`
(b) `overset~T=1/2muv_(rel)^2=1/2mu|vecv_1-vecv_2|^2`
So, `overset~T=1/2mu(v_1^2+v_2^2)`