A ship A is moving Westwards with a speed of 10 km h

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A ship A is moving Westwards with a speed of 10 km h^–1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h^–1. The time after which the distance between them becomes shortest, is :

1. 5 h
2. 5 √2 h
3. 10 √2 h
4. 0 h

Correct Option: A

V^{^→}_A = 10(-î)
V^{^→}_A = 10(ĵ)
V^{^→}_BA = 10ĵ + 10î = 10 √2 km / h
Distance OB = 100 cos 45° = 50 √2 km

Time taken to reach the shortest distance between A and B

=	OB^{^→}	=	50 √2	= 5h
	V^{^→}_BA		10 √2