Aplane flies due north (90° from east) with a velocity of 100 km/h for 3 hours. during this time, a steady wind blows southeast at 30 km/h at an angle of 315° from due east. after 3 hours, where will the plane’s position be relative to its starting point? show your work.

244.78 km, 74.9⁰ North East

Explanation:

Step 1: identify the given parameters

Velocity of plane = 100 km/h

Velocity of wind = 30 km/h

Time of flight = 3 hours

Distance traveled by plane = (100 km/h)*(3 hours) = 300 km

Distance blew by wind = (30 km/h)*(3 hours) = 90 km

Step 2: construct a triangle with the distance of plane and wind as show in the imaged uploaded.

Step 3: calculate the final position (R) of the plane

Using cosine rule, calculate R

R² = 300² + 90² -2(300X90)cos315

R² = 98,100 - 54,000cos315

R² = 98,100 - 38,183.766

R² = 59,916.234

R = √59,916.234

R = 244.78 km

Step 4: calculate the direction of the plane(Ф)

Using sine rule, calculate the direction of the plane

= 74.9⁰ North East

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