Physics

Physics

Problem

A wind blows with a speed of 40 km h−140\,\text{km}\,\text{h}^{-1} in a direction making 150∘150^{\circ} with the positive x-axis (angles measured anticlockwise from the x-axis). a. (i) Express the wind velocity vector in unit-vector form Vx i^+Vy j^V_x\,\hat i + V_y\,\hat j. b. (ii) If each component is rounded to the nearest whole number of kilometres per hour, find the magnitude of the rounded vector. c. (iii) Calculate the percentage error in this magnitude with respect to the actual speed of 40 km h−140\,\text{km}\,\text{h}^{-1}.
Intuitive explanation

Wind velocity is a vector, so you need to break it into its x and y components using the angle given. The key insight is that the 150°150° angle tells you the direction of the wind in standard position—use cos⁡\cos and sin⁡\sin with that angle to find how much of the wind's speed points east versus north. Once you have the components, you can work with them independently or recombine them as needed.

Intuitive explanation

Wind velocity is a vector, so you need to break it into its x and y components using the angle given. The key insight is that the 150°150° angle tells you the direction of the wind in standard position—use cos⁡\cos and sin⁡\sin with that angle to find how much of the wind's speed points east versus north. Once you have the components, you can work with them independently or recombine them as needed.

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