Assumption: The unit "ms⁻²" for velocity is a typo and should be "ms⁻¹". We will proceed with velocities u1 = 70 ms^-1 and u2 = 55 ms^-1.

Here's how to solve the problem using the principle of conservation of momentum. Assumption: The unit "ms⁻²" for velocity is a typo and should be "ms⁻¹". We will proceed with velocities u_1 = 70 ms^-1 and u_2 = 55 ms^-1. The principle of conservation of momentum states that for a collision where bodies stick together, the total momentum before the collision equals the total momentum after the collision. The formula is: m_1 u_1 + m_2 u_2 = (m_1 + m_2) V where m_1 and m_2 are the masses, u_1 and u_2 are their initial velocities, and V is their common final velocity. Given: m_1 = 30 kg u_1 = 70 ms^-1 m_2 = 40 kg u_2 = 55 ms^-1 a) Same direction before collision Step 1: Apply the conservation of momentum principle. Since both bodies are moving in the same direction, their velocities are both positive. (30 kg)(70 ms^-1) + (40 kg)(55 ms^-1) = (30 kg + 40 kg) V Step 2: Calculate the total initial momentum. 2100 kg ms^-1 + 2200 kg ms^-1 = (70 kg) V 4300 kg ms^-1 = (70 kg) V Step 3: Solve for the common final velocity V. V = 4300 kg ms^-170 kg V = (430)/(7) ms^-1 V ≈ 61.428 ms^-1 Rounding to one decimal place: V ≈ 61.4 ms^-1 b) Opposite direction, before collision Step 1: Apply the conservation of momentum principle. If the bodies move in opposite directions, one velocity must be negative. Let's assume u_1 is positive and u_2 is negative. (30 kg)(70 ms^-1) + (40 kg)(-55 ms^-1) = (30 kg + 40 kg) V Step 2: Calculate the total initial momentum. 2100 kg ms^-1 - 2200 kg ms^-1 = (70 kg) V -100 kg ms^-1 = (70 kg) V Step 3: Solve for the common final velocity V. V = -100 kg ms^-170 kg V = -(10)/(7) ms^-1 V ≈ -1.428 ms^-1 Rounding to one decimal place: V ≈ -1.4 ms^-1 The negative sign indicates that the combined mass moves in the direction of the initially heavier body (40 kg mass). Send me the next one 📸