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A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 381 km from Athens in the direction 22° N of E. The pilot heads directly for Sparta and flies at an airspeed of 151 km/h. After flying for 2.52 h, the pilot expects to be at Sparta, but instead he finds himself 16 km due west of Sparta. He has forgotten to correct for the wind. (a) What is the velocity of the plane relative to the air? (b) Find the velocity (magnitude and direction) of the plane relative to the ground. (c) Find the wind speed and direction. Please be thorough.

A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 381 km from Athens in the direction 22° N of E. The pilot heads directly for Sparta and flies at an airspeed of 151 km/h. After flying for 2.52 h, the pilot expects to be at Sparta, but instead he finds himself 16 km due west of Sparta. He has forgotten to correct for the wind. (a) What is the velocity of the plane relative to the air? (b) Find the velocity (magnitude and direction) of the plane relative to the ground. (c) Find the wind speed and direction. Please be thorough.

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A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 381 km from Athens in the direction 22° N of E. The pilot heads directly for Sparta and flies at an airspeed of 151 km/h. After flying for 2.52 h, the pilot expects to be at Sparta, but instead he finds himself 16 km due west of Sparta. He has forgotten to correct for the wind. (a) What is the velocity of the plane relative to the air? (b) Find the velocity (magnitude and direction) of the plane relative to the ground. (c) Find the wind speed and direction. Please be thorough.
Transcribed Image Text:A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 381 km from Athens in the direction 22° N of E. The pilot heads directly for Sparta and flies at an airspeed of 151 km/h. After flying for 2.52 h, the pilot expects to be at Sparta, but instead he finds himself 16 km due west of Sparta. He has forgotten to correct for the wind. (a) What is the velocity of the plane relative to the air? (b) Find the velocity (magnitude and direction) of the plane relative to the ground. (c) Find the wind speed and direction. Please be thorough.
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