Question

A plane flies at 350 mph in the direction 40° north of east, with a wind blowing at 40 mph in the 70° south of east. What is the plane’s drift angle? 5. 89° 6. 38° 45. 89° 46. 38°.

Answer 1

The plane's drift angle is (a) $5.89^o$

The given parameters are:

$S_p = 350m/h$ --- the speed of the plane

$S_w = 40m/h$ --- the speed of the wind

$d_p = N40^oE$ ---- the direction of the plane

$d_w = S70^oE$ ---- the direction of the wind

Start by resolving the components of the motion of the plane and of the wind, as follows:

$S_p=350 \times \sin(40)i +350 \times \cos(40)j$ ---- for the plane

$S_p=224.98i +268.12j$

$S_w=40 \times \sin(70)i -40 \times \cos(70)j$ --- for the wind

$S_w=37.59i -13.68j$

Add the resolution of vectors

$S = S_p + S_w$

$S = 224.98i + 37.59i + 268.12j - 13.68j$

$S = 262.57i + 254.44j$

Next, we calculate the plane's direction as follows:

$\theta = \tan^{-1}(\frac{262.57}{254.44})$

$\theta = 45.90^o$

Rewrite as:

$\theta = N45.90^oE$

The drift angle is then calculated as:

$D = \theta -d_p$

This gives

$D = N45.90^oE - N40^oE$

$D = N5.90^oE$

Rewrite as:

$D = 5.90^o$

Hence, the plane's drift angle is (a) $5.89^o$

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