Question

3. 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. Determine the magnitude and direction of the boat's overall velocity.

Answer 1

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 :

$v=\sqrt{5^2+3^2} \\\\=\sqrt{25}\\\\=5\ \text{metres/minute}$

For direction,

$\tan\theta=\dfrac{v_y}{v_x}\\\\=\dfrac{3}5{}\\\\\theta=\tan^{-1}(\dfrac{3}5{})\\\\=30.96^{\circ}$

Hence, this is the required solutin.