Question

An Airplane is heading due south at a speed of 580 km/h. If a wind begins blowing from the southwest at a speed of 130 km/h (average), calculate the following.
(a) the velocity (magnitude and direction) of the plane relative to the ground
(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action.

Please I have no idea how to do this and knowone will help me.

Answer 1

direction of wing would be 45' opposite from the direction of plane so simply \[130/\sqrt{2}\] would be the effective speed of wind opposing the plane.
then the speed of the plane would be 530-\[130/\sqrt{2}\] Km/hr and direction of plane would be south east.
with this speed you can calculate how much behind the plane is from its assumed position.
if plane moves at a speed mentioned above in direction southeast which is 45' away from its original direction for 10min.
and calculate the difference betwen distance travelled in both cases using Pythagoras eqn

Answer 2

@theyatin : the direction of the resultant velocity won't be exactly southeast, will it? Because I got my velocity vector diag looking like this :

since the magnitude of the 2sides is not equal, the angles opposite to them also wont be. so they cant be 45, right?