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^i−50^j) km/hr ∴t=−(80^i+150^j).(−40^i−50^j)|−40^i−50^j|2 =3200+75004100 hr=107004100 hr=2.6 hrs

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