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  4. A boat goes across a river with a velocity 12 km/h . The magnitude of its resultant speed in flowing water is 13 km/h . The velocity of water flow in the river is

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Q. A boat goes across a river with a velocity $ 12\,km/h $ . The magnitude of its resultant speed in flowing water is $ 13 \,km/h $ . The velocity of water flow in the river is

AMUAMU 2012Motion in a Plane

Solution:

Resultant speed $ v_{br}= v_b + v_r$
$v_{br} = \sqrt{v_b^2 + v_r^2}$
$(13)^2 = (12)^2 + v_r^2$
$v_r^2 = 169 - 144$
Velocity of water in the river
$v_r = \sqrt{25} = 5\,km/h$