A jet airliner, flying initially 300 mi/hr due
east, suddenly enters a region where the
wind is blowing 100 mi/hr, pushing the
aircraft in the direction 30° north of east.
What is the resultant speed of the aircraft?

For us to find the resultant speed of the aircraft, we will simply add the vector components of the wind and the vector velocity of the aircraft to get;

V = v_xi^ + v_yj^

Now,

v_xi^ = (300 + 100cos30°)i^

v_yj^ = (100 sin 30°) j^

This gives;

v_xi^ = 386.6 i^

v_yj^ = 50 j^

Thus;

V = 386.6 i^ + 50 j^

Resultant velocity is;

|V| = √(386.6² + 50²)

|V| = √151959.56

|V| = 389.82 mi/hr

A jet airliner, flying initially 300 mi/hr due east, suddenly enters a region where the wind is blowing 100 mi/hr, pushing the aircraft in the direction 30° north of east. What is the resultant speed of the aircraft?

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A jet airliner, flying initially 300 mi/hr due
east, suddenly enters a region where the
wind is blowing 100 mi/hr, pushing the
aircraft in the direction 30° north of east.
What is the resultant speed of the aircraft?