Water Flows from a Tank of Constant Cross-Sectional Area $50 \mathrm { At } ^ { 2 }$

question 35

Multiple Choice

Water flows from a tank of constant cross-sectional area $50 \mathrm { At } ^ { 2 }$ through an orifice of constant cross-sectional area $\frac { 1 } { 4 } \mathrm { ft } ^ { 2 }$ located at the bottom of the tank. Initially, the height of the water in the tank was $20 \mathrm { ft }$ , and $t$ sec later it was given by the equation
$$2 \sqrt { h } + \frac { 1 } { 25 } t - 2 \sqrt { 20 } = 0 \quad 0 \leq t \leq 50 \sqrt { 20 }$$
How fast was the height of the water decreasing when its height was $2 \mathrm { ft }$ ?

• A) \(\quad 100 \sqrt { 5 } - 50 \sqrt { 2 } \mathrm { ft } / \mathrm { sec }\)
• B) \(100 \sqrt { 5 } - 50 \sqrt { 2 } \mathrm { ft } / \mathrm { sec }\)
• C) \(\frac { 2 } { 25 } \mathrm { ft } / \mathrm { sec }\)
• D) \(\frac { \sqrt { 2 } } { 25 } \mathrm { ft } / \mathrm { sec }\)

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