Question

The current in a river is flowing from east to west at 4.5 km/h. On this river, a single remote controlled boat is heading north, perpendicular to the current at 6.7 km/h. If you were standing on the edge of the bank observing this boat, how fast and in what direction is the boat traveling?

Answer 1

Using relative motion

Speed of boat w.r.t ground = speed of boat w.r.t current + speed of current w.r.t ground

Vbg = Vbc + Vcg

Now given that

Vbc = 6.7 km/h due north

Vbc = (6.7 km/h) j

Vcg = 4.5 km/h due west

Vcg = (-4.5 km/h) i

So Using these

Vbg = (6.7 km/h) j + (-4.5 km/h) i

Vbg = -4.5 i + 6.7 j

So speed of boat will be

|Vbg| = sqrt ((-4.5)^2 + 6.7^2) = 8.07 km/h

Direction of bboat will be

Direction = arctan (6.7/4.5) = 56.11 deg

Since Vbg is in 2nd quadrent, So direction will be North of West

Which means

Speed = 8.07 km/h, heading 56.11 deg North of West

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