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Question

A boat is sent across a river with a velocity of 3 km/h. If the resultant velocity of the boat is 5 km/h, then velocity of the river flow is

A
8 km/h
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B
10 km/h
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C
6 km/h
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D
4 km/h
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Solution

The correct option is D 4 km/h
From the relation we have
vb,r=vbvr ...(i)
given that velocity of boat w.r.t river is
vb,r=3 km/h ^j
Let the direction of river flow is along +ve x axis,
hence velocity of river w.r.t ground is vr km/h ^i

The velocity of boat w.r.t ground is
vb=vb,r+vr
vb=3 ^j+vr ^i
Hence resultant speed,
|vb|=32+v2r,
given that |vb|=5 km/h
52=32+v2r
v2r=259=16
vr=16=4 km/h

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