# At what height should the hole be made in the drum to maximize the horizontal distance of splash down point and drum?

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A small hole is made in the side of a full oil drum (barrel of 1m tall). A jet of oil shoots from the drum and lands on the ground some distance from the drum. At what height (in metres) above the ground should the hole be made to maximize the horizontal distance between the splash down point and the drum?

posted Mar 21, 2017

Explanation
let it be at a height y
the vertical velocity of jet at exit is zero and horizontal velocity =sqrt(2g(1-y))
therefore horizontal distance covered in time t is x=sqrt(2g(1-y))*t.................................................(1)
also time to cover distance y due to acceleration g from zero vertical velocity is t=sqrt(2y/g)...........(2)
substitute this value of t in (1)
x=sqrt(2(1-y)2y) OR x^2=4(y-y^2)
x is max when x^2 is maximum
differentiate and equate to zero
you get y=1/2

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