CATAGORY: Mechanics QUESTION: I think this question is Kinematics... A jet pilot sets his compass due east. After 30 min, during which he maintained a constant speed of 400km/h with repect to the air, he finds himself flying over a city located 220 km east and 20km south of his point of departure, Determine the wind velocity in magnitude and direction.

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From the figure 1. below we see that in the X direction (east) the plane travels 220km in 0.5hours (30min) and -20km in the Y direction (south) . We will apply the basic formula relating position to time for a constant velocity. (1) d = vt distance = velocity X time. This is a vector formula so we can break this up into X and Y components of motion to give (2) x = V(x)t y = V(y)t where x = location to the east of the starting point y = position to the north of the starting position note:if y is negative then the position is south of the starting position. V(x) = east component of velocity V(y) = north component of velocity (see note on y) Now the plane flies due east at 400km/hr with respect to the air but is also being carried aling by the wind so we have (3) V(x) = 400km/hr + V(x,wind) V(y) = 0km/hr + V(y,wind) where V(x,wind) and V(y,wind) are the x and y coordinates of the wind with respect to the ground. Substituting these into (2) gives (4) x = (400km/hr + V(x,wind))t y = V(y,wind)t now lets substitute some numbers into (4). From figure 1. x = 220km y = -20km t = 0.5hr so (5) 220km = (400km/hr + V(x,wind)) X 0.5hr -20km = V(y,wind) X 0.5hr figure 1. \ 220km >-->- .................................... ^ y / . | . | \ . | >-->- . 20km -------> x / . .\ >-->- / Solving (5) for V(x,wind) and V(y,wind) gives (6) V(x,wind) = 220km/0.5hr -400km/hr = 40km/hr V(y,wind) = -20km/0.5hr = -40km/hr ***************************** * * * V(x,wind) = 40km/hr * * V(y,wind) = -40km/hr * * * ***************************** This means the wind is comming out of the north-west and blowing toward the south-east. The magnitude of the wind velocity is |V| = sqrt( (40km/hr)^2 + (-40km/hr)^2) = 56.6 km/hr ************************ * * * |V| = 56.6km/hr * * * ************************ (note: sqrt means square root and a^2 means a times a.)

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