Final answer:
To determine the distance the jar will sink when submerged in water, we need to calculate its volume and use Archimedes' principle. The jar will sink by the weight of the water it displaces divided by the weight per unit area of the jar. To find the volume of honey needed for all but 0.00000075% of the jar to be below the water's surface, we can calculate the volume based on the density of honey compared to water.
Step-by-step explanation:
To determine how far the jar will sink when submerged in water, we can first calculate its volume. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Since the jar has a diameter of 4.75 miles, the radius is half of that, so r = 2.375 miles. Similarly, the height is 1.25 miles. Substituting these values into the volume formula, we get V = π(2.375^2)(1.25) = 9.3649 cubic miles.
Next, we need to convert this volume from cubic miles to cubic centimeters. Since 1 mile is approximately equal to 160934.4 centimeters, 1 cubic mile is equal to (160934.4)^3 cubic centimeters. So, the volume of the jar in cubic centimeters is 9.3649 * (160934.4)^3 cm³.
To calculate the distance the jar will sink, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The weight of the water displaced by the jar is equal to the volume of water (in cm³) multiplied by its density. The density of water is 1.075 g/cm³. Therefore, the weight of the water displaced is (9.3649 * (160934.4)^3) * 1.075 g.
Finally, we can calculate the distance the jar will sink by dividing the weight of the water displaced by the weight per unit area of the jar. The weight per unit area of the jar is equal to its density multiplied by the thickness. The thickness of the jar is given as 0.75 inches, so we need to convert this to centimeters using the conversion factor 2.54 cm/inch. Therefore, the weight per unit area of the jar is (0.75 * 2.54) cm * 2.72 g/cm³. Dividing the weight of the water displaced by the weight per unit area of the jar will give us the distance the jar will sink when submerged in water.
For the second part of the question, we need to find the volume of honey that will cause all but 0.00000075% of the jar to be below the surface of the water. Since the density of honey is 3.45 times that of water, the density of honey is 3.45 * 1.075 g/cm³. Using the same calculation as before, we can find the volume of honey that will cause all but 0.00000075% of the jar to be below the surface of the water.