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Question

http://loncapa2.physics.sc.edu/res/sc/gblanpied/courses/usclib/hrw8/hrwpictures/15-42.jpg A tank is filled with water to a height H, 34 m. A hole is punched in one of the walls at a depth h, 9.18 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

m g (H-h) = 1/2 m v^2 g(H-h) = 1/2 v^2 v = (2g(H-h))^1/2 the v is horizontal so x = v*t t is the time it takes to fall the distance h h = 1/2 g t^2 t = (2h/g)^1/2 so x = (2g(H-h))^1/2 * (2h/g)^1/2 = ( 2g(H-h) * 2h/g )^1/2 = ( 4 h(H-h) )^1/2 = 2( h(H-h) )^1/2 putting the values 21.34m

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