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Question:

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

5√2h

10√2h

0 h

5 h

Solution:

→VA = -10^i
→VB = 10^j
→VB/A = →VB - →VA
→VB/A = 10^j + 10^i = 10√2(^i + ^j/√2)
The shortest distance is ac, which will be at time when B reaches point c from b,
t = bc/VB/A = 100/√2 / 10√2 = 5h