Step 1:

A pilot wanting to travel northeast.

Wind is blowing from the west.

Therefore, direction of wind speed is towards east.

Triangle law of vectors addition:

If the two vectors represented by the two adjacent sides of triangle, then the third side of the triangle determines the addition of the two vectors as shown.

Wind speed is towards east direction.

The airplane should move in the north-east direction.

If the airspeed is moving in north direction, then the resultant component of north and east gives northeast direction.

Hence the airspeed should direct in north direction so that airplane moves in the north-east direction.

Therefore, airspeed is in north direction.

Solution:

First option is correct.

2) \ \ Airspeed of airplane is kmph.

Wind is blowing from the coast out to sea at kmph.

Wind is blowing from the coast out to sea means that it opposes the air speed.

Therefore, resultant relative speed of airplane is kmph.  

Airplane is km off the coast above the sea. 

Distance traveled by the plane to reach the shore is km. 

.  

Substitute km and kmph in the expression.

hr. \ \  

. 

Therefore, time taken by the plane to reach the shore is . 

Solution: 

Option (c) is correct.