Question

A ship (pt B) is trying to travel in a north-west direction (45 degrees from North). The water current (pt A) is flowing due east with a velocity of 2 mph. The magnitude of the relative velocity of the ship to the current is 5 mph. Express the direction of the ship’s velocity vector relative to the water in unit vector form.

rA)

Answer 1

The water velocity,vw= 2 mph.

The magnitude of the relative velocity of the ship to the currentvr= 5 mph

ships velocity=5+2=7mph

It is customary to introduce special notation for unit vectors of the positive x and y axis.

i=<1,0>

j=<0,1>

i and j are called standard basis vectors

So, v(a,b)=ai+bj=7 cos $\theta$ i + 7 sin $\theta$ j