Question

If a body of mass 4 kg moves at a velocity of 25 m/s and has a completely inelastic collision with a body of mass 10 kg, the final velocities of both the bodies is 14 m/s. Calculate the initial velocity of the body of mass 10 kg.

Answer 1

We are given the following information about an inelastic collision.

Mass of 1st object = 4 kg

Mass of 2nd object = 10 kg

Initial velocity of 1st object = 25 m/s

Final velocity of both objects = 14 m/s

Initial velocity of 2nd object = ?

In an inelastic collision, the momentum is conserved but the kinetic energy is not conserved.

Recall that the total momentum is conserved and given by

$m_1u_1+m_2u_2=(m_1+m_2)v_2$

Let us substitute the given values and solve for initial velocity of the body (u2)

$\begin{gathered} m_1u_1+m_2u_2=(m_1+m_2)v_2 \\ 4\cdot25+10\cdot u_2=(4+10)\cdot14 \\ 100+10\cdot u_2=196 \\ 10\cdot u_2=196-100 \\ 10\cdot u_2=96 \\ u_2=\frac{96}{10} \\ u_2=9.6\; \frac{m}{s} \end{gathered}$

Therefore, the initial velocity of the body of mass 10 kg is 9.6 m/s