A motor car of width w moves uniformly along a straight road , parallel to the pavement almost touching it. A pedestrian on the edge of the pavement at a distance l ahead of the car begins to walk uniformly to cross the road . If v is the speed of the car and u is the speed of the pedestrian relative to the road , show that the pedestrian can cross the road safely in front of the car
if u > v sin (alpha) , where (alpha) = tan^-1 (w/l).
Let B be the position of the pedestrian on edg of pavement. A is position of car on the road (consider car as a point on pavement ). Given AB=I unit. Let B' is point opposite to point B on the therside of the road.Let pedestrian crosses road by making an angle `pi/2-alpha` to ine joining BB' perpendicular to pavement and reaches at ponit C.Thus
Thus car has to travell dstance =`I+W cot(alpha)`
pedestrian has to travel=`Wcosec(alpha)`
Pedestrian just cross road infront of the car then