Answered

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Will a truck that is 14 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one-way road that passes under the bridge shown in the figure on the right?

Will A Truck That Is 14 Feet Wide Carrying A Load That Reaches 12 Feet Above The Ground Clear The Semielliptical Arch On The Oneway Road That Passes Under The B class=

Sagot :

Given the equation of an elipse

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

from the question,

[tex]\begin{gathered} \text{major axis}\Rightarrow2a \\ \therefore2a=52 \\ a=\frac{52}{2}=26ft \\ b=13ft \end{gathered}[/tex]

Given that

[tex]x=14ft[/tex]

Substitute, for a,b, and x in the elipse formula to find y

[tex]\begin{gathered} \frac{14^2}{26^2}+\frac{y^2}{13^2}=1 \\ \frac{196}{676}+\frac{y^2}{169}=1 \end{gathered}[/tex]

Multiply through by 169

[tex]\begin{gathered} 49+y^2=169 \\ y^2=169-49 \\ y^2=120 \\ y=\sqrt[]{120}=10.95ft \end{gathered}[/tex]

Hence, it clear the arch because the height of the archway of the bridge 7 feet from the center is approximatelyfeet

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