1.

Find expression for final velocities when two bodies of same mass m have head on collision when moving in opposite direction with equal speeds. Assuming the collision to be elastic.

Answer»

Head on collision : When a body moving in a straight line collides with another body moving in the same straight line, the collision is called head-on collision.

Here \(v_1=\frac{(m_1-m_2)u_1+2m_2u_2}{m_1+m_2}\)

\(\frac{(m-m)v+2m(-v)}{m+m}\)

\(\frac{0-2mv}{2m}\)

i.e., v1 = -v

Similarly, \(v_2=\frac{(m_2-m_1)u_2+2m_1u_1}{m_1+m_2}\)

\(\frac{(m-m)(-v)+2mv}{m+m}\)

\(\frac{0+2mv}{2m}\)

i.e. v2 = v

After collision the bodies bounce back with same initial speed, i.e., v.



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