Question

A boat sails at 10 km / hr northeast on a river that flows east at 3 km / hr.
What is the magnitude and direction of the speed of the boat relative to the Earth's surface?

Answer 1

Here,

let east is the positive x direction and north is the positive y direction

velocity of boat relative to river, vbr = 10 * (cos(45) i + j * sin(45))

vbr = 7.07 i + 7.07 j km/hr

flow of river, vr = 3 i km/hr

Now, for the speed of boat relative to Earth's surface

vb = vbr + vr

vb = 7.07 i + 7.07 j + 3 i = 10.07 i + 7.07 j

vb = sqrt(10.07^2 + 7.07^2) at atan(7.07/10.07) degree north of east

vb = 12.3 km/hr at 35.1 degree north of east

the magnitude of speed of boat is 12.3 km/hr and direction of 35.1 degree north of east .