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 47.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 21.5 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

1515 lb =687.1924 kg

1125 lb= 510.2914 kg

21.5 ft=6.5532 m

Momentum before = momentum after:

687.19v1 - 510.29kg*169.2km/hr = 1197.48kg*V
½*(687.19kg+510.29kg)*V² = (687.19kg+510.29kg)*9.8m/s²*0.75*6.55m = 57,649.68J => V = 9.81m/s = 35.316km/hr
687.19v1 - 510.29kg*169.2km/hr = 1197.48kg*35.316km/hr
680v1 = 510.29kg*169.2km/hr + 1197.48kg*35.316km/hr
v1 = (510.29kg*169.2km/hr + 1197.48kg*35.316km/hr)/687.19kg = 187.18km/hr
How fast (in miles per hour) was car A traveling just before the collision?
v1 = 187.18km/hr 116.30826 miles/hr

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