A boat is heading due north across a river with aspeed of 12.0 km/h relative to the water. The water inthe river has a uniform velocity of 6.00 km/h due eastrelative to the ground. Determine the velocity of theboat relative to an observer standing on either bank.

The velocity of the boat relative to an observer standing on either bank = (12î + 6j) km/h

In layman terms, the velocity of the boat relative to an observer standing on either bank is 13.42 km/h in the 26.6° North of East direction.

Explanation:

Relative velocity of body A with respect to body B, Vab, is given as Va - Vb.

where Va and Vb are velocities of A and B with respect to an external frame of reference.

That is,

Vab = Va - Vb

For this, question, let the observer be our external frame of reference (very convenient as the observer is stationary and not moving)

Let Vb = velocity of boat with respect to our external frame of reference (the observer/the ground) = ?

Va = velocity of the water of the river with respect to our external frame of reference (the observer/the ground) = 6 km/h east = (6j) km/h

Vba = velocity of the boat relative to the river = 12 km/h north = (12î) km/h

Vba = Vb - Va

12î = Vb - 6j

Vb = (12î + 6j) km/h

Magnitude = √[12² + 6²] = 13.42 km/h

Direction = tan⁻¹ (6/12) = 26.6°