The nose of an ultralight plane is pointed south, and its airspeed indicator sho

Question

The nose of an ultralight plane is pointed south, and its airspeed indicator shows 26 m/s . The plane is in a 11 m/s wind blowing toward the southwest relative to the earth.

A) Letting x be east and y be north, find the components of v P/E (the velocity of the plane relative to the earth). Express your answers using two significant figures separated by commas. vx, vy =

B) Find the magnitude of vP/E. Express your answer using two significant figures.

C) Find the direction of vP/E. Express your answer using two significant figures.

Explanation / Answer

The plane vector components are (0 , - 26)

The Wind components are assuming SW means 180 degrees + 45 or 225 degrees or 45 degrees below the - x axis in the 3rd quadrant

cos 45 = x/11

0.707 = x/11

x = 7.778 m/s in the 3rd quadrant ==> - 7.778

sin 45 = y/11

0.707 = y/11

y = 7.778 m/s in 3rd quadrant ====> - 7.778

Add the vectors for the plane

Vx = 0 + ( - 7.778) = - 7.778 m/s

Vy = (- 26 + ( - 7.778) = -33.778 m/s

So the total components for the plane is (-7.778, - 33.778)       ..............Ans (a)

from Pythagorean Theorem :-

vP/E^2 = 7.778^2 + 33.778^2

vP/E = 34.66 m/s              ................Ans(b)

tan^-1 = 33.778/7.778

tan^-1 = 4.343

angle = 77 degrees

below the +x axis in the 4th quadrant or 360 deg - 77 deg = 283 deg          .........Ans(c)

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