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Question

A man swims across a river with speed of 5 km/hr with respect to the river in positive y direction, while a boat goes upstream with speed 12 km/hr with respect to the river in negative x direction. How fast and in which direction does the man appear to go to the boatman ? Given that the velocity of flowing water is 2 km/hr in positive x direction.

A
13 km/hr in a direction making angle tan1(512) with x-axis
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B
13 km/hr in a direction making angle tan1(512) with y-axis
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C
13 km/hr in a direction making angle tan1(34) with x-axis
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D
13 km/hr in a direction making angle tan1(34) with y-axis
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Solution

The correct option is A 13 km/hr in a direction making angle tan1(512) with x-axis
Given that velocity of man w.r.t. the boat is 5^j
vmr=5^j
Also velocity of the boat w.r.t the river vbr=12 ^i
And velocity of the river = 2^i
Hence velocity of man w.r.t. the boat is
vmrvbr=5^j+12^i

Magnitude of the resultant =52+122=13 km/hr
Direction with x axis :
tanθ=vyvx=512
θ=tan1512


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