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A ship is sailing towards the north a...

A ship is sailing towards the north at a speed of 1.25 m/s. The current is taking it towards the east at the rate of 1 m/s and a sailor is climbing a vertical pole on the ship at the rate of 0.5 m/s. Find the velocity of the sailor in space.

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Verified by Experts

The correct Answer is:
`1.677` m`//`sec.
We take the unit vectors `hati, hatj and hatk` parallel to the east, north and vertically upwards in the direction of pole, respectively. Then the velocity vectors of the current, ship and the sailor are, respectively, `hati, 1.25hatj and 0.5hatk`. Velocity `vecv` of the sailor in space is the resultant of these vectors. Hence,
`vecv= hati+ 1.25hatj+ 0.5 hatk`
Then `|vecv|= sqrt(1+ (1.25)^(2) + (0.5)^(2))`
`" "=sqrt(1+ 1.5625 + .25)`
`" " = sqrt(2.8125)` = 1.677 m/s
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