1. **State the problem:** We need to find the magnitudes of the force components $u$ and $v$ given a force of 300 N acting at angles 30° with the horizontal axis $u$ and 15° with the vertical axis $v$. 2. **Understand the force components:** The force vector $F = 300$ N can be resolved into two perpendicular components along $u$ (horizontal) and $v$ (vertical). 3. **Use trigonometry:** Since the force makes a 30° angle with $u$, the component along $u$ is: $$u = 300 \times \cos(30^\circ)$$ Similarly, since the force makes a 15° angle with $v$, the component along $v$ is: $$v = 300 \times \cos(15^\circ)$$ 4. **Calculate the components:** $$u = 300 \times \cos(30^\circ) = 300 \times \frac{\sqrt{3}}{2} \approx 300 \times 0.866 = 259.81$$ $$v = 300 \times \cos(15^\circ) \approx 300 \times 0.966 = 289.80$$ 5. **Interpretation:** The force components are approximately $u = 259.81$ N along the horizontal axis and $v = 289.80$ N along the vertical axis. **Final answer:** $$u \approx 259.81 \text{ N}, \quad v \approx 289.80 \text{ N}$$