(a)(i) Linear momentum is the product of the mass of a body and its velocity.
(ii) Impulse is the product of a large force and short time for which the force acts.
(b) The principle of conservation of linear momentum states that in system of colliding bodies the total momentum of the system is constant provided no external forces act on the system.
(c) (i) \(m_1u_1 + m_2U_2 = v(m_1 + m_2)\) 5 x 10\(^{3}\) x 3 + 0
= v(5 x 10\(^{3}\) + 2.5 x 10\(^{3}\)) v = \(\frac{15 \times 10^3}{7.5 \times 10^3}\) = 2m/s
(ii) Initial K.E = \(\frac{1}{2}mv^2 = \frac{1}{2} MV^2 = \frac{1}{2} times 5 \times 10^{3} \times 3^2\)
= 2.25 x 10\(^4\)
Final K.E = \(\frac{1}{2}mv^2 = \frac{1}{2} (5 + 2.5) \times 10^3 \times 2^2\)
= 1.5 x 10\(^{4}\)J
Loss in K.E of the couple = (2.25 - 1.5) x 10\(^4\)
= 75 x 10\(^3\)J
(iii) Impulse = (\(mu_1U_1 + m_2U_2\)) - v
(\(mu_1 +m_2) (0 + 5 \times 10^3) - 2 (2.25 + 5) 10^3\) = 0Ns