Water is filled up to a height of 12 m in a tank having vertical side walls. A hole is made in one of the walls at a depth h below the water level. The value of h for which the emerging stream of water strikes the ground at the maximum range is m.

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6. Given: water depth H=12 m, hole at depth h below the surface, so the hole is H-h above the ground. Torricelli gives the horizontal launch speed v=√2gh, and the jet falls H-h in time t=√(2(H-h))/g. Range R=vt=2√h(H-h). The product h(H-h) is largest when the two factors are equal, at h=H/2. h=(12)/2=6 m, and the maximum range is then R=H=12 m.

Water is filled up to a height of 12 m in a tank having vertical side walls. A hole is made in one of the walls at a depth h below the water level. The value of h for which the emerging stream of water strikes the ground at the maximum range is ______ m.

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