An equilateral prism of wood with specific gravity 0.620 is placed into a freshwater pool. The prism has a side of s. y Yd of the depth of submersion when the Yu Determine the ratio Ya prism is pointed down to the depth of submersion when the prism is pointed up. Yu

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Chapter1: Units, Trigonometry. And Vectors
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**Title: Understanding the Submersion of an Equilateral Prism in Water**

**Introduction:**
An equilateral prism of wood with a specific gravity of 0.620 is placed into a freshwater pool. The prism has a side length of \( s \).

**Objective:**
Determine the ratio \(\frac{y_d}{y_u}\) of the depth of submersion when the prism is pointed down to the depth of submersion when the prism is pointed up.

**Diagram Explanation:**
The image displays two diagrams of an equilateral prism partially submerged in water. The left diagram shows the prism oriented with the vertex pointing downward, creating a submerged depth labeled \( y_d \). The right diagram shows the prism oriented with the base pointing downward, creating a submerged depth labeled \( y_u \). Both diagrams indicate the position of the waterline and the dimensions of the sides.

**Calculation:**
Evaluate and find the ratio \(\frac{y_d}{y_u}\).

**Solution Box:**
Provide the solution for the ratio \(\frac{y_d}{y_u}\) in the adjacent box.

**Conclusion:**
Understanding how various orientations affect the submersion depth of an object with non-uniform density and shape is an important aspect of fluid mechanics and buoyancy studies.
Transcribed Image Text:**Title: Understanding the Submersion of an Equilateral Prism in Water** **Introduction:** An equilateral prism of wood with a specific gravity of 0.620 is placed into a freshwater pool. The prism has a side length of \( s \). **Objective:** Determine the ratio \(\frac{y_d}{y_u}\) of the depth of submersion when the prism is pointed down to the depth of submersion when the prism is pointed up. **Diagram Explanation:** The image displays two diagrams of an equilateral prism partially submerged in water. The left diagram shows the prism oriented with the vertex pointing downward, creating a submerged depth labeled \( y_d \). The right diagram shows the prism oriented with the base pointing downward, creating a submerged depth labeled \( y_u \). Both diagrams indicate the position of the waterline and the dimensions of the sides. **Calculation:** Evaluate and find the ratio \(\frac{y_d}{y_u}\). **Solution Box:** Provide the solution for the ratio \(\frac{y_d}{y_u}\) in the adjacent box. **Conclusion:** Understanding how various orientations affect the submersion depth of an object with non-uniform density and shape is an important aspect of fluid mechanics and buoyancy studies.
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