Physics 1 word problem ch 8

Question

You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighss1515lb and was traveling eastward. Car B weighs 1125lb and was traveling westward 45mph. 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 pavement to be 0.750.

What speed v(in miles per hour) was car A traveling just before the collision? (English units)

Answer 1

Let v_A is speed of car A before collision. Moution after collision: 0 - (m_A + m_B)v²/2 = -- μ(m_A + m_B)gs;

v = (2μgs)^1/2 =(2·0.750·32.174ft/s²·20.5ft)^1/2 = 31.454 ft/s = 31.454·0.682mi/h = 21.452 mi/h.

By law of conservation of impulse 1515v_A - 1125·45 = (1515 + 1125)·21.452.

v_A = 70.798 mi/h