1. The problem involves finding the components of a velocity vector where the resultant velocity is 90 km/h pointing northwest (NW), and there is an eastward wind velocity. 2. Since NW is at a 45° angle between north and west, the velocity vector components can be considered along north and west axes. 3. The 90 km/h velocity is the hypotenuse of a right triangle formed by the north and west components of the velocity. 4. Let the eastward wind velocity be $v_e$ km/h, and the northward component of the velocity be $v_n$ km/h. 5. The westward component must overcome the eastward wind, so the westward velocity component $v_w$ satisfies $v_w = v_e + x$, where $x$ is the velocity relative to the wind. 6. Using Pythagoras theorem for the right triangle with hypotenuse 90 km/h: $$90^2 = v_n^2 + v_w^2$$ 7. Since the vector points NW, $v_n = v_w$ (because NW is 45°, components equal), so: $$90^2 = 2 v_n^2 \implies v_n = \frac{90}{\sqrt{2}} = 63.64 \text{ km/h}$$ 8. The westward component $v_w = 63.64$ km/h must overcome the eastward wind $v_e$, so the actual velocity relative to the ground is: $$v_w = v_e + x = 63.64$$ 9. To find $x$, subtract the wind velocity $v_e$ from 63.64 km/h. Final answer: The components of the velocity vector are approximately 63.64 km/h north and 63.64 km/h west, with the westward component reduced by the eastward wind velocity $v_e$ to maintain the 90 km/h NW resultant velocity.