Two boats are travelling along a river.Boat A is half as massive as boat B,but the kinetic energy of boat A is 3 larger than the kinetic energy of boat B.What is the ratio of their speeds v_A/v_B?

Question

Quizplus · Accepted Answer

The kinetic energy (KE) is given by KE = 0.5 * m * v^2. Let m_A and m_B be the masses of boats A and B, and v_A and v_B be their speeds. Given m_A = 0.5 * m_B and KE_A = 3 * KE_B, we have 0.5 * m_A * v_A^2 = 3 * (0.5 * m_B * v_B^2). Substituting m_A = 0.5 * m_B, we get 0.5 * (0.5 * m_B) * v_A^2 = 3 * (0.5 * m_B * v_B^2). Simplifying, v_A^2 = 6 * v_B^2, so v_A/v_B = sqrt(6) ≈ 2.4.

Two Boats Are Travelling Along a River