Question

A 1500 kg hatchback is heading south on a north-south street and runs into an SUV of mass 2200 kg heading west through the same intersection. At the time of the crash, the two vehicles stick together and go off together. The coefficient of kinetic friction between the tires and the street is given to be 0.750. The policeman arriving on the scene of the accident finds that the two vehicles slid 6.43 m south and 5.32 m west of the impact point before coming to rest.

Find the initial velocities of each of the vehicles just before the crash.

Answer 1

V_1, m_1 rightarrow hatchback 1500 kg V_2, m_2 rightarrow SU v 2200 kg conservation of energy 1/2 m_1 V^2_1 + 1/2 m_1 V^2 = Work_friction Work_friction = f_k times Distance = 27750 times 8.35 = 231712.5 J Also 1/2 m_1 V^2_1/1/2 m_2 V^2_2 = 6.43/5.32 V^2_1/V^2_2 = 6.43 times 2200/5.32 times 1500 v_1 = 1.33 V_2 using this value in 1 V_1 = 1.33 V_2 = 12.9 m/s f_k/f_N = 0.75 (mu_k) 1/2 times 1500 times (1.33 V_2)^2 + 1/2 times 2200 times V^2_2 = 231712.5 V_2 = 9.77 m/s