Shortest distance between the two points in motion:
The shortest distance between them is obtained by taking perpendicular distance of one of the points from relative path of the 2nd with respect to the 1st.
Example: At a specific instant 2 aeroplanes are at the distance of 250 kilometre, one due east of the other. The 1st one is moving towards west at the rate of 100 km/hr and the 2nd with velocity of 75 km/hr towards the south. Find time when they are nearest to each other and least distance between them.
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Solution: AB = 250 km
v1 = 100 km/hr, v2 = 75 km/hr
also BM = (AB) cosθ
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= 250 x 100/125 = 200 km => time = 200/125 hr that is 1 hour 36 minutes.
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