Question

a construction worker needs to know how fast water will flow through a pipe. he can find this value using the formula ( v=sqrt{2 g h} ), where ( v ) is the velocity in meters per second, ( g ) is the acceleration due to gravity in meters per second ( ^{2} ), and ( h ) is the height in meters of the water above the opening. (a) on earth, the acceleration due to gravity is approximately ( 10 mathrm{~m} / mathrm{s}^{2} ). which function represents the velocity of the water on earth? a ( v=sqrt{20 h} ) b ( v=sqrt{2 h} ) c ( v=sqrt{20 g} ) d ( v=sqrt{2 g} ) (b) what is the velocity of the water if the height of the water above the opening is 23 meters tall? a ( 21.45 mathrm{~m} / mathrm{s} ) b ( 102.86 mathrm{~m} / mathrm{s} ) c ( 6.78 mathrm{~m} / mathrm{s} ) d ( 32.53 mathrm{~m} / mathrm{s} )

Explanation:

(a)

Step1: Sustituir el valor de \(g\) en la fórmula

Dado que \(g = 10\space m/s^{2}\), sustituimos en la fórmula \(v=\sqrt{2gh}\).
$$v=\sqrt{2\times10\times h}$$

Step2: Simplificar la expresión

Multiplicamos \(2\times10 = 20\).
$$v=\sqrt{20h}$$

Step1: Sustituir \(h = 23\) en la fórmula \(v=\sqrt{20h}\)

$$v=\sqrt{20\times23}$$

Step2: Calcular el producto dentro de la raíz

\(20\times23=460\).
$$v = \sqrt{460}$$

Step3: Calcular la raíz cuadrada

\(\sqrt{460}\approx21.45\) (usando una calculadora).

Answer:

A. \(v = \sqrt{20h}\)

(b)