1. The problem asks to express the velocity vectors $v$ (plane in still air) and $w$ (wind) in terms of their magnitudes and direction angles. 2. The plane flies at 179 mph on a bearing of N42°E. Bearing N42°E means 42° east of north, so the angle with the positive y-axis is 42°. 3. The wind blows from west to east at 50 mph, which means it is along the positive x-axis (0° from x-axis). 4. To express vectors in terms of $i$ (x-direction) and $j$ (y-direction), use: $$v = |v|(\sin \theta \mathbf{i} + \cos \theta \mathbf{j})$$ where $\theta = 42^\circ$ is the angle east of north. 5. For the wind vector $w$, blowing east (0° from x-axis): $$w = |w|(\cos 0^\circ \mathbf{i} + \sin 0^\circ \mathbf{j}) = 50(1 \mathbf{i} + 0 \mathbf{j}) = 50 \mathbf{i}$$ 6. Substitute values: $$v = 179(\sin 42^\circ \mathbf{i} + \cos 42^\circ \mathbf{j})$$ $$w = 50(\cos 0^\circ \mathbf{i} + \sin 0^\circ \mathbf{j})$$ 7. Comparing with options, this matches option A. **Final answer:** A. $v = 179 \sin 42^\circ \mathbf{i} + 179 \cos 42^\circ \mathbf{j};\quad w = 50 \sin 0^\circ \mathbf{i} + 50 \cos 0^\circ \mathbf{j}$