Answer to Question #273004 in Physics for mattythehon

Question

The police are investigating an accident. They have determined that the mass of car A is 2275 kg and the mass of car B is 1525 kg. From the skid marks and the data for the friction between the tires and concrete, the police determined that the cars , when locked together, hand a velocity of 31 km/h at an angle of 43 degrees North of the eastbound street. If the speed limit was 35 km/h on both streets:

a) should one or both cars be ticketed for speeding? Prove

b) Which car had the right of way at the intersection? Explain

c) Was one driver or both drivers at fault for the accident? Explain

Answer 1

a) Apply momentum conservation:

$$N: m_Av_{AN}+m_Bv_{BN}=(m_A+m_B)u_N,\\ E:m_Av_{AE}+m_Bv_{BE}=(m_A+m_B)u_E.\\\space\\ N: m_Av_{AN}+m_B·0=(m_A+m_B)31\sin43°,\\ E:m_A·0+m_Bv_{BE}=(m_A+m_B)31\cos43°.$$

We know the masses, so, we can find the speeds:

$$v_{AN}=35.3\text{ km/h},\\ v_{BE}=56.5\text{ km/h}.$$

Both should be ticketed.

b) Car A had the right way of intersection because it was to the right of car B.

c) Both drivers are guilty because both exceeded the speed limit.