Answer:
0.033 ft
Step-by-step explanation:
Let g = 32.2 ft/s2 and h be the maximum height that water can be filled before the sides shatter.
Pressure is distributed from 0 to maximum at the bottom like the following equation:
[tex]P = \rho gh[/tex]
So the force generated by water pressure on the side of the tank is
[tex]F = PA = \rho ghs/2[/tex]
where s = 6ft is the side length of the tank. This force cannot be larger than 200lb
[tex]\rho ghs/2 \leq 200[/tex]
[tex]62.4*32.2*h*6/2 \leq 200[/tex]
[tex]h \leq 0.033 ft[/tex]
The distance the in which the water will reach before it shatters will be 1.03ft
Data;
Using integration, the force at any depth y is 62.4y lb/ft^3
[tex]200 = \int\limits^d_0 {62.4y} \, 6dy\\ 200 = \int\limits^d_0 {374.4y} \, dy\\ 200 = \int\limits^6_0 {374.4y} \, dy\\ 200 = [374.4/2 y^2]_0^d\\200 = 187.2(d^2 - 0)\\200 = 187.2d^2\\d^2 = 200/187.2\\d = 1.03ft[/tex]
From the calculations above, the distance in which the water will reach before it shatters is 1.03ft
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