Explanation:
A boat at sea is being moved by the ocean current at 5 metres/minute directly to the east.
At the same time, it is being moved directly to the north at 3 metres/minute by a strong wind.
We need to find the magnitude and direction of the boat's overall velocity.
As both velocities are moving perpendicular to each other. The resultant velocity is given by :
[tex]v=\sqrt{5^2+3^2} \\\\=\sqrt{25}\\\\=5\ \text{metres/minute}[/tex]
For direction,
[tex]\tan\theta=\dfrac{v_y}{v_x}\\\\=\dfrac{3}5{}\\\\\theta=\tan^{-1}(\dfrac{3}5{})\\\\=30.96^{\circ}[/tex]
Hence, this is the required solutin.
