Question

You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 1515 lb and was traveling eastward. Car B weighs 1125 lb and was traveling westward at 42.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 20.5 ft before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750 . How fast (in miles per hour) was car A traveling just before the collision? (This problem uses English units because they would be used in a U.S. legal proceeding.) (answer in mph!!)

Answer 1

mass of car A,

mass of car B,

velocity of car B,

-Ve sign indicates that it is moving in the opposite direction to the car A.

velocity of car A,

After collision, both cars moved together with mass M=m_A+m_B, with the velocity of V.

So, the kinetic energy can be estimated from the energy lost due to work done by kinetic friction.

where are the kinetic frictional coeficient and the distance that the both cars moved before coming to rest.

By equating this value with the momentum conservation expressions, we can calculate the speed of car A as follows,

Hence, the car A was moving along eastward with initial speed of 68.5 mph.