Question

A ship sets sail from Rotterdam, The Netherlands, intending to head due north at 8.5 m/s relative to the water. However, the local ocean current is 1.50 m/s in a direction 40.0º north of east and changes the ship's intended motion. What is the velocity of the ship relative to the Earth?

Answer 1

Step-by-step explanation:

Given

Velocity of ship relative to water is
`8.5 \m/s`

`V_(sw)=V_(s)-V_(w)=8.5\hat{j}----1`

Velocity of water with respect to earth

`V_(we)=V_(w)-V{e}=1.5(\cos (40)\hat{i}+\sin (40)\hat{j})----2`

adding 1 and 2

`V_(s)-V_(e)=1.5\cos (40)\hat{i}+8.5\hat{j}+1.5\sin (40)\hat{j}`

`V_(s)-V_(e)=1.5\cos (40)\hat{i}+9.46\hat{j}`

`|V_(se)|=√((1.149)^2+(9.46)^2)`

`|V_(se)|=√(90.8118)`

`|V_(se)|=9.53\ m/s`