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?

389.82 mi/hr

Step-by-step explanation:

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

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