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