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Q.

After being kicked by a footballer, a ball started to fly straight towards the goal at velocity υ = 25 m/s making an angle α=370 with the horizontal. Due to side wind blowing at u = 10 m/s perpendicular the initial velocity of the ball, the ball had deviated from its initial course by s = 2 m by the time it reached the plane of the goal. Find the time that it took the ball to reach the plane of the goal, if the goal was situated at distance L = 32 m from the footballer.(Drag force of air is side ways g=10m/sec2  )

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answer is 1.8.

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Detailed Solution

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Motion in ground frame

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Motion in wind frame
In wind frame goal post shift by ut
 

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uvcosα=utSL

Lvcosα=tSu

t=Su+Lvcosα=1.8 sec

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