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quiz_10A

quiz_10A - dy dt =-1 72 √ y Solve this equiation to ﬁnd...

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Math 213 — Quiz 10 Name Solution 1. Let y ( t ) and V ( t ) be the height and volume of water in a tank at time t . If water leaks through a hole with area a at the bottom of the tank, then Torricelli’s Law says that dV dt = - a p 2 gy where g is the acceleration due to gravity. Suppose the tank is cylindrical with height 6 ft and radius 2 ft and the hole is circular with radius 1 in. If we take g = 32 ft / s 2 . then y satisﬁes the diﬀerential equation
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Unformatted text preview: dy dt =-1 72 √ y. Solve this equiation to ﬁnd the height of water at time t , assuming the tank is full at time t = 0. The equation is separable, we can rewrite it as dy √ y =-dt 72 . Integrating both sides, we ﬁnd 2 √ y =-t 72 + C. Since y (0) = 6 ft we ﬁnd that C = 2 √ 6. Therefore, y = ± √ 6-t 144 ² 2 ....
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