A ship A is moving Westwards with a speed of 10 kmh-1and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h-1. The time after which the distance between them becomes shortest, is

Given situation is shown in the figure. Velocity of ship AvA=10 km h-1towards west Velocity of ship BvB=10 km h-1towards north OS = 100 kmOP = shortest distanceRelative velocity between A and B isvAB=vA2+vB2=102 km h-1cos45°=OPOS;12=OP100OP=1002=10022=502 kmThe time after which distance between them equals to OP is given byt=OPvAB=502102⇒t=5 h