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Question

Ship A is sailing towards north-east with velocity v=30^i+50^j km/hr where ^i points east and ^j towards north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. Time in which A will be at minimum distance from B is

A
2.2 hrs
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B
4.2 hrs
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C
2.6 hrs
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D
3.2 hrs
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Solution

The correct option is C 2.6 hrs

vA=(30^i+50^j) km/hr
vB=10^i km/hr; rA=0^i+0^j
rB=(80^i+150^j) km
Time after which distance between them will be minimum
t=rBA.vBA|vBA|2;
Where rBA=(80^i+150^j) km
vBA=10^i(30^i+50^j)=(40^i50^j) km/hr
t=(80^i+150^j).(40^i50^j)|40^i50^j|2
=3200+75004100 hr=107004100 hr=2.6 hrs

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