Physics
Physics
Problem
An aircraft has an air-speed of directed east of north. A steady wind of blows towards the east. a. (i) Resolve the aircraft’s air-speed and the wind velocity into rectangular components, taking the –axis towards the east and the –axis towards the north. b. (ii) Hence obtain the ground velocity (resultant velocity) of the aircraft in component form, and calculate its magnitude and true heading (angle measured east of north). c. (iii) The pilot wishes to reach a point that is due north of the present position. Estimate the time taken to reach this point with the wind blowing as stated.Intuitive explanation
This is a vector addition problem where you need to find the aircraft's actual motion relative to the ground by combining its velocity through the air with the wind's velocity. The key insight is to set up a coordinate system (north and east), break both the plane's airspeed and wind into components, then add them vectorially to get the ground velocity. Once you have the resultant, you can find its magnitude and direction.
Intuitive explanation
This is a vector addition problem where you need to find the aircraft's actual motion relative to the ground by combining its velocity through the air with the wind's velocity. The key insight is to set up a coordinate system (north and east), break both the plane's airspeed and wind into components, then add them vectorially to get the ground velocity. Once you have the resultant, you can find its magnitude and direction.