Question

A boat is headed north at a velocity of 8 km h-1. A strong wind is blowing whose pressure on the boat’s superstructure causes it to move sideways to the west at a velocity of 2 km h-1. There is also wave present that flows in a direction 30° south of east at a velocity of 5 km h-1. What is the velocity of the boat?​

Answer 1

The velocity of the boat moving at the given conditions is 5.97 km/h at 67⁰.

The given parameters;

• velocity of boat northwards, = 8 km/h
• velocity of the boat westwards, = 2 km/h
• velocity of the wind, = 5 km/h 30° south of east

The resultant vertical velocity of the boat is calculated as;

$v_y = 8 \ - \ 5 sin(30)\\\\v_y = 8 - 2.5\\\\v_y = 5.5 \ km/h$

The resultant horizontal velocity of the boat is calculated as;

$v_x = -2 \ + 5cos(30)\\\\v_x = 2.33 \ km/h$

The resultant boat velocity is calculated as follows;

$v = \sqrt{v_x^2 + v_y^2} \\\\v = \sqrt{2.33^2 + 5.5^2} \\\\v = 5.97 \ km/h$

The direction of the velocity;

$\theta = tan^{-1} (\frac{v_y}{v_x} )\\\\\theta = tan^{-1}(\frac{5.5}{2.33} )\\\\\theta = 67 \ ^0$

Thus, the velocity of the boat moving at the given conditions is 5.97 km/h at 67⁰.

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