You have been called to testify as an expert witness in a trial involving a head

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 45.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 22.5 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.)

Explanation / Answer

Weight of Car A = 1515 lb

Weight of Car B = 1125 lb

VA = ?

VB = 45.0 mph

Initial Momentum Of Cars, = 1515 * Va - 1125 *45.0

Now, After Collision , both the cars move together.

Initial Velocity = v

Final Velocity = 0

Friction Force = u*N

F = u*m*g

a = F/m = u*g

a = 0.750 *g

S = 22.5 ft

V^2 = U^2 - 2*a*S

U = sqrt(2*0.750*32.15*22.5) ft/s

U = 32.94 ft/s

Final Momentum of the system = (1515 + 1125) * 32.94

Using Momentum Conservation -

1515 * Va - 1125 *45.0 = (1515 + 1125) * 32.94

Va = 90.8 mph
Speed of Car A just before the collision, Va = 90.8 mph

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