Question

A boat travels 30 miles north, 20 miles east and 40 miles northeast. What is the angle of rotation of the boats direction from start to finish

Answer 1

The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.

Explanation:

Let x axis be east direction and x axis be north direction.

The boat first travels 30 miles north

⇒ Displacement = 30 j

Then boat travels 20 miles east

⇒ Displacement = 20 i

And at last the boat travels 40 miles north east

⇒ Displacement = 40·cos 45 i + 40·sin 45 j

= 28.28 i + 28.28 j

Total displacement = 48.28 i + 58.28 j

`\text{Angle, tanθ = }(58.28)/(48.28)`

⇒ θ = 50.36⁰

Hence, The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.