Question

A glider aircraft initially traveling due west at 84.0 km/h encounters a sudden gust of wind at 34.5 km/h directed toward the northeast.

What are the speed and direction of the glider relative to the ground during the wind gust? (The velocity of the glider with respect to the ground is the velocity of the gilder with respect to the wind plus the velocity of the wind with respect to the ground.)

Answer 1

Since one vector is at west and other at north- east, the angle between them is 135 degree

Resultant speed, $v = \sqrt{v_1^2 + v_2^2 + 2 v_1 v_2 \cos \theta}$

Substituting : $v = \sqrt{84.0^2 +34.5^2 + 2 *84.0*34.5 \cos 135^0} = 64.4 km/h$

Resultant angle is given by,

-1 o = tan U2 sin(180º – 0) U1 + x2 cos(1800 - 0)

Substituting : $\phi = \tan^{-1}\left [ \frac{34.5 \sin (180^0 - 135^o)}{84.0 -34.5 \cos (180^0 - 135^o) } \right ] =22.56^0$

22.56 degree north of west