A tank is filled with water to a height H, 24 m . A hole is punched in one of th

Question

A tank is filled with water to a height H, 24 m. A hole is punched in one of the walls at a depth h, 7.68 m, below the water surface. 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

Height of the water in the tank H = 24 m

Depth of the hole fromthe surface of the water h = 7.68 m

Height of the hole from the base point h '= H - h

                                                          = 16.32 m

Speed of the water from the hole v = (2gh ') 1/ 2

Where g = 9.8 m/ s 2

Substitute values weget v = 17.88 m / s

Required distance or range R = v t

where t = time taken to reach the ground

            = ( 2h '/ g ) ( 1/ 2)

            = 1.824 s

So, R = 32.63 m

(b). Required depth from the surface of the water = H - h

                                                                       = 16.32 m

           =

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