An airplane pilot sets a compass course due west and maintains an airspeed of 221km/h . After flying for a time of 0.490h, she finds herself over a town a distance 125km west and a distance 13km south of her starting point.
FIND THE MAGNITUDE OF WIND VELOCITY.
v = ___ km/h
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To find the magnitude of the wind velocity, we need to determine how the wind affected the motion of the airplane.
Let's consider the horizontal component of the airplane's motion. The airplane set a compass course due west and maintained an airspeed of 221 km/h. This means that in still air, the airplane's horizontal velocity would be 221 km/h west.
However, due to the presence of wind, the actual ground track of the airplane is different. Given that the town is located 125 km west and 13 km south of the starting point, we can determine the displacement of the airplane caused solely by the wind.
Using the Pythagorean theorem, the displacement caused by the wind is given by:
displacement = √(west^2 + south^2)
= √(125^2 + 13^2)
= √(15625 + 169)
= √15894
≈ 126.09 km
Since the airplane flew for a time of 0.490 hours and the displacement caused by the wind is 126.09 km, we can calculate the magnitude of the wind velocity using the formula:
magnitude of wind velocity = displacement / time
= 126.09 km / 0.490 h
≈ 257.34 km/h
Therefore, the magnitude of the wind velocity is approximately 257.34 km/h.