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 θ = 14.0°, that the cars were separated by distance d = 25.0 m when the driver 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 v0 = 18.0 m/s. With what speed did car A hit car B if the coefficient of kinetic friction was (a) 0.570 (dry road surface) and (b) 0.190 (road surface covered with wet leaves)?

Answer 1

F=mgsinα –F(fr)=
= mgsinα - μmgcosα
a=F/m =g(sinα – μcosα)
=9.8(sin14-0.57•cos14)= -3.04 m/s²
v²=v₀²+2ad
v=sqrt{ v₀²+2ad} =
=sqrt{18²+2• (-3.04) •25}=13.1 m/s