# Two ships are 10 km apart on a line running south to north. The one farther north is streaming west at 40 km/hr. The other is steaming north at 40 km/hr. The distance of closest approach and how long do they take to reach it are is(a) 7.071 km, 1/2 hr(b) 7.071 km, 1/8 hr(c) 6 km, 1/8 hr(d) none of these

Siddhartha Mukherji
24 Points
7 years ago
Let the first ship steaming north be named A and the other B. The relative velocity of A with respect to B is 40√2 south west.  If we extend the line along the 45° south west from the initial position of A, the distance of closest approach is the perpendicular drawn from B to this line.
So, the distance of closest appraoch = 10 sin 45° = 10/√2 = 7.07 m
Yash srivastav
13 Points
4 years ago
•ship A streaming towards west at 40km/h
•ship B streaming towards north at 40km/h
•using relative velocity give velocity of A to B by reversing it at an angle of 45°
•then find magnitude :-√(40)^2+(40)^2=40√2
•to find min distance draw line perpendicular to
magnitude from point A.
•S min = 10sin45°=10*1/√2=10/√2 or 5√2