Question:
A plane is flying west with and air speed of 70.0 m/s. The is a wind blowing at 20.0 m/s at an angle of 36 degrees south of east. What is the velocity of the plane relative to the ground?
I normally understand these questions but only when the wind is blowing with the plane. How do you solve it if it is going against the plane. AND how to you change the vectors into x and y, that would probably help… unless that is wrong?
Draw the plane flying to the left with 70 m/s. Draw the wind blowing from like this \ at a 36 degree angle, at 20 m/s.
The plane has a 70 m/s component west and a 0 m/s component south.
The wind can be thought of as having a 20cos(36) m/s component east and a 20sin(36) m/s component south.
The resulting speed of the plane is 70 – 20cos(36) m/s west and 20sin(36) m/s south
That is 53.82 m/s west and 11.76 m/s south
The total speed = sqrt(53.82^2 + 11.76^2) = 55.09 m/s
The angle is arctan(11.76/53.82) = 12.33 degrees south of west.
February 20th, 2010 at 2:56 am
Draw the plane flying to the left with 70 m/s. Draw the wind blowing from like this \ at a 36 degree angle, at 20 m/s.
The plane has a 70 m/s component west and a 0 m/s component south.
The wind can be thought of as having a 20cos(36) m/s component east and a 20sin(36) m/s component south.
The resulting speed of the plane is 70 – 20cos(36) m/s west and 20sin(36) m/s south
That is 53.82 m/s west and 11.76 m/s south
The total speed = sqrt(53.82^2 + 11.76^2) = 55.09 m/s
The angle is arctan(11.76/53.82) = 12.33 degrees south of west.
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