WAEC Further Mathematics 2024 Paper

Concept:The law of conservation of momentum states that the total momentum of two colliding bodies remains constant if no external force acts on them. Because the second body moves in the opposite direction, its velocity is taken as negative.Explanation:Let $m_1 = 80 \, \mathrm{kg}$ and $m_2$ be the masses of the first and second bodies.Initial velocities are $u_1 = 25 \, \mathrm{m\,s^{-1}}$ and $u_2 = -10 \, \mathrm{m\,s^{-1}}$ because they move in opposite directions.After collision, the common velocity is $v = 12.8 \, \mathrm{m\,s^{-1}}$.Using conservation of momentum:$$m_1u_1 + m_2u_2 = v(m_1 + m_2)$$Substitute the values:$$80(25) + m_2(-10) = 12.8(80 + m_2)$$Simplify the terms:$$2000 - 10m_2 = 1024 + 12.8m_2$$Rearrange to collect $m_2$ terms on one side:$$2000 - 1024 = 12.8m_2 + 10m_2$$$$976 = 22.8m_2$$Therefore:$$m_2 = \frac{976}{22.8} = 42.8 \, \mathrm{kg}$$Correct to the nearest whole number, $m_2 \approx 43 \, \mathrm{kg}$.Answer:The mass of the second body is $43 \, \mathrm{kg}$.Correct option: C. 43 kg.