An aircraft can maintain a speed of relative to still air
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
An aircraft can maintain a speed of 300km h−1 relative to still air. A wind of 80km h−1 is blowing from the south-west (that is, from 225∘ measured clockwise from the north). The pilot wishes the resultant ground track of the aircraft to be due north.
(i) Express the wind velocity vector in terms of eastward i and northward j components.
(ii) Let the aircraft head be at an angle θ east of north. Write the velocity of the aircraft relative to the air in component form in terms of θ.
(iii) Using vector addition, find the value of θ (to the nearest 0.1∘) that will ensure a due-north ground track, and compute the corresponding ground speed of the aircraft.