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A balloon starts rising from earth surface with constant speed v0. Due to wind the balloon gathers a horizontal velocity component vx= ay where a is a positive constant and y is its height above earth surface. Find the horizontal drift of balloon as a function of height.

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a

av0y2

b

a2v0y2

c

av0y3

d

a3v0y2

answer is B.

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Detailed Solution

due to uniform speed in y direction, its height as a function of time= y=v0tIn x-distance vx=ay=av0t ⇒t=yv0dxdt=av0t∫0x dx=∫0t av0tdtx=av0t22x=av02yv02=a2v0y2

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A balloon starts rising from earth surface with constant speed v0. Due to wind the balloon gathers a horizontal velocity component vx= ay where a is a positive constant and y is its height above earth surface. Find the horizontal drift of balloon as a function of height.