I have the following problem: A helicopter capable of flying at a speed of 100km per hour in still air takes off from O for a mining town located at A. The position vector of A relative to O is 200i-300j km. Throughout the journey, the helicopter encounters a wind blowing with velocity 13i + 5j km per hour. Find the velocity vector the pilot should set so that the helicopter flies directly to A and find the time taken for this journey.
I know how to solve for the velocity vector which works out to be 43.635i -89.96j, but I am unsure of how to find the time taken. Any help would be much appreciated.
Add the velocity vector to the wind vector to get the resultant vector, which is the helicopter's actual velocity. Then divide the distance to $A$ by the magnitude of the resultant vector.