Notes O Ask Your Teacher 5 points KatzPSEr1 3.P.062. A glider aircraft initially

Question

Notes O Ask Your Teacher 5 points KatzPSEr1 3.P.062. A glider aircraft initially traveling due west at 77.0 km/h encounters a sudden gust of wind at 41.5 km/h directed toward the northeast (see the figure below). 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.) magnitude direction km/h o north of west glider 45 Wind Need Help?Read It

Explanation / Answer

Given that

Speed of glider w.r.t wind is 77 km/hr due west

V_Gw = -77 km/h i

Speed of wind w.r.t to ground is given that 41.5 km/h directed northeast, So

V_wg = 41.5*cos 45 deg i + 41.5*sin 45 deg j

V_wg = 29.34 km/h i + 29.34 km/h j

Now Speed of glider w.r.t ground will be

V_Gg = V_Gw + V_wg

V_Gg = -77 km/h i + 29.34 km/h i + 29.34 km/h j

V_Gg = -47.66 i + 29.34 j

So,

|V_Gg| = sqrt ((-47.66)^2 + 29.34^2)

|V_Gg| = 55.97 km/h

Direction will be

Direction = arctan (29.34/47.66)

Direction = 31.62 deg North of west

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