Question

A ship sets sail from Rotterdam, The Netherlands, intending to head due north at 6.5 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:

velocity of ship with respect to water = 6.5 m/s due north

`\overrightarrow{v}_(s,w)=6.5 \widehat{j}`

velocity of water with respect to earth = 1.5 m/s at 40° north of east

`\overrightarrow{v}_(w,e)=1.5\left ( Cos40\widehat{i} +Sin40\widehat{j}\right)`

velocity of ship with respect to water = velocity of ship with respect to earth - velocity of water with respect to earth

`\overrightarrow{v}_(s,w) = \overrightarrow{v}_(s,e) - \overrightarrow{v}_(w,e)`

`\overrightarrow{v}_(s,e) = 6.5 \widehat{j}- 1.5\left (Cos40\widehat{i} +Sin40\widehat{j} \right )`

`\overrightarrow{v}_(s,e) = - 1.15 \widehat{i}+5.54\widehat{j}`

The magnitude of the velocity of ship relative to earth is
`\sqrt{1.15^(2)+5.54^(2)}` = 5.66 m/s