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.
If`u = v sin (alpha)` , show that the pedestrian can cross the road just in front of the car , by walking relative to the road in a direction making an angle `(pi)/ 2 - (alpha)` with the direction of the motion of the car relative to the road.
Let A be position of the car and B is position of the man.The distance between A and B is I (given).Let B' is point on the opposite side of the point B.Let man crosses road by making an angle `alpha` with BB' and reaches point C .Thus
and B'C=`W tan(alpha)`
`(W sec(alpha))/u=(I+W tan(alpha))/v`
`` It will not possible otherwise he will never cross the road.
Thus pedestrian must move by making an angle (pi/2-alpha) with the direction of motion of car.