Physics

Problem

An aircraft can maintain a speed of

300\;\text{km h}^{-1}

relative to still air. A wind of

80\;\text{km h}^{-1}

is blowing from the south-west (that is, from

225^{\circ}

measured clockwise from the north). The pilot wishes the resultant ground track of the aircraft to be due north. a. (i) Express the wind velocity vector in terms of eastward

\mathbf{i}

and northward

\mathbf{j}

components. b. (ii) Let the aircraft head be at an angle

\theta

east of north. Write the velocity of the aircraft relative to the air in component form in terms of

\theta

. c. (iii) Using vector addition, find the value of

\theta

(to the nearest

0.1^{\circ}

) that will ensure a due-north ground track, and compute the corresponding ground speed of the aircraft.

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