You testify as an expert witness in a case involving an accident in which car A

Question

You testify as an expert witness in a case involving an accident in which car A slid into the rear of car B. which was stopped at a red light along a road headed down a hill (see the figure). You find that the slope of the hill is theta = 13.0 degree, that the cars were separated by distance d = 23.0 m when the drive' of car A put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car A at the onset of braking was V_0 = 17.0 m/s. With what speed did car A hit car B if the coefficient of kinetic friction was 0.600 (dry road surface) and 0.180 (road surface covered with wet leaves)?

Explanation / Answer

First we find the grade of the road. The slope is 13º so the tan(13) = 0.231. This will take away from the available friction since it is downhill.

a) Vo = 17 m/s, d = 23 m, f = -0.60 + 0.231 = -0.369 g

V = sqrt(Vo^2 + 2gdf)
= sqrt(17^2 - 2(9.8)(23)(0.369)) : Note the sign change
= 11.074 m/s

b) Vo = 17 m/s, d =23 m, f = -0.18 + .231 = 0.051 g (now an acceleration)

V = sqrt(17^2+2(9.8)(23)(.051))
= 22.78 m/s

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