Question

A ship moves due North at 100km/h on a river flowing due East at 25km/h. Calculate the magnitude of the resultant velocity of the ship and it direction.

Answer 1

We can find the magnitude of the resultant velocity of the ship from the Pythagorean theorem:

$$v_{res}=\sqrt{v_{river}^2+v_{ship}^2}=\sqrt{(25\ \dfrac{km}{h})^2+(100\ \dfrac{km}{h})^2}=103\ \dfrac{km}{h}.$$

We can find the direction of the resultant velocity from the geometry:

$$\theta=tan^{-1}(\dfrac{v_{river}}{v_{ship}}),$$ $$\theta=tan^{-1}(\dfrac{25\ \dfrac{km}{h}}{100\ \dfrac{km}{h}})=14^{\circ}\ N\ of\ E.$$