A tank is filled with water to a height H, 36 m . A hole is punched in one of th

Question

A tank is filled with water to a height H, 36 m. A hole is punched in one of the walls at a depth h, 12.96 m, below the water surface (see the figure). What is the distance x from the base of the tank to the point at which the resulting stream strikes the floor?

Could a hole be punched at another depth to produce a second stream that would have the same range? If so, at what depth?

At what depth should a hole be punched to make the emerging stream strike the ground at the maximum distance from the base of the tank?

Explanation / Answer

Part A:

the distance is

2*sqrt(h(H-h)) = 2*sqrt(12.96*(36-12.96)) = 34.56  m

Part B:

Assuming a hole be punched at another depth to produce a second stream that would have the same range, we can write

2*sqrt(h'(H-h')) = 2*sqrt(h(H-h))

Simplifying, h'(H-h') = h(H-h)

Solving the above quadratic equation gives us

h' = H-h --> answer

part C:

maximum range the emerging stream could reach, taking derivative of (2*sqrt(h*(H-h)) with respect to the depth h :

simplifying gives,

h_max = H/2

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