If the riverboat is crossing the river, with a velocity of 4 m/s along the north and the river is flowing with a velocity of 3 m/s along the west,
then what is the magnitude and direction of resultant velocity?
A
5 m/s in south-east direction
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B
7 m/s in north-west direction
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C
5 m/s in north-west direction
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D
7 m/s in south-east direction
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Solution
The correct option is C 5 m/s in north-west direction We know that the magnitude of resultant can be calculated by
R=√Vrb2+Vr2+2Vrb×Vrcosθ
(By triangular law of vector addition)
where, Vrb= velocity of riverboat
and Vr= velocity of river
but here θ=90∘
So, R=√32+42 ⇒R=5m/s
For the direction, we can calculate
α=tan−1(VrVrb)=tan−1(34)=36.87ο
So, here we get the direction of resultant velocity as 36.87° in north-west direction.
So, option C is correct.