Question

a ship is heading due north at 7.50 m/s relative to the water. The local current is 1.52 m/s in a direction 42 degree west of north. Find its velocity relative to earth( find both direction and magnitude of the velocity)

Answer 1

V=7.5 m/s
v=1.52 m/s
u=?
u(x)=V(x)+v(x)= 0-vsin42⁰= - 1.52•0.67=-1.02 m/s
u(y)=V(y)+v(y)= V+vcos42⁰=7.5+1.52•0.0.74=8.63 m/s
u=sqrt{u(x)²+ u(y)²}=8.69 m/s
tanβ = u(x)/u(y)=1.02/8.63=0.12
β =6.74⁰ (west of north)