Distance of closest approach of two ships problem
Two ships are 10 km apart on a line running south to north. The one farther north is steaming west at 20 km/h. The other is steaming north at 20 km/h. What is their distance of closest approach? How long do they take to reach it?
Solution and Answer:
The main hindrance to solving problem is that students fail to visualize the situation.
Let’s represent the condition using a diagram.
Let the first ship steaming north be named A and the other B. The relative velocity of A with respect to B is 20 √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
Time taken to reach the distance of closest approach = distance of closest approach / relative speed
= (10/√2)/(20 √2)
= 0.25 h