Question

Problem 2 A car and a truck collide on a very slippery highway. The car, with a mass of 1600 kg, was initially moving at 50 mph. The truck, with a mass of 3000 kg, hit the car from behind at 65 mph. Assume the two vehicles form an (a) If, immediately after the collision, the vehicles separate and the truck's velocity is found to be 55 mph in (b) If instead the vehicles end up stuck together, what will be their common velocity immediately after the isolated system in what follows. the same direction it was going, how fast (in miles per hour) is the car moving? collision?

Answer 1

Given that m_1 = 1600 kg, m_2 = 3000 kg u_1 = 50 mph, u_2 = 65 mph (a) v_1 = ? v_2 = 55 mph Conservation of linear momentum. m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 1600 times 50 + 3000 times 65 = 1600 times v_1 + 3000 times 55 275, 000 = 1600 v_1 + 165,000 1600 v_1 = 110,000 v_1 = 110,000/1600 Therefore v_1 = 68.75 mph. (b) Conservation of linear momentum m_1 u_1 + m_2 u_2 = (m_2 + m_2) V v = m_1 u_1 + m_2 u_2/(m_1 + m_2) = 1600 times 50 + 3000 times 65/(1600 + 3000) = 275,000/4600 Therefore v = 59.78 mph.