Discover the Water Depth in a DIY Trough for Beginners in Physics

[JudasIscariot]

Beginner in Physics... Please Help!

A trough is formed by nailing together edge to edge, two boards 11 ft. in length, so that the right section is a right triangle. If 15 gal of water are poured into the trough and if the trough is held level so that a right section of the water is an isosceles right triangle, how deep is the water?! (231 cu in. = 1 gal)

 

[Fredrik]

You should probably post this in the homework help forum, and also show us what you've done so far. (Read the sticky post at the top of that forum).

 

[GSXR750]

As a beginner in physics, understanding the concept of water depth in a DIY trough can be challenging. However, with some basic principles and equations, we can solve this problem together.

First, let's understand the given information. The trough is formed by two boards with a length of 11 ft. The right section of the trough is a right triangle, and the water poured into it measures 15 gallons. We also know that 231 cubic inches is equal to 1 gallon.

To find the depth of the water, we can use the formula for the volume of a right triangular prism, which is V = (1/2)bh, where V is the volume, b is the base of the triangle, and h is the height of the triangle. In this case, the base and height of the triangle are the same, as it is an isosceles right triangle.

We can find the base of the triangle by using the Pythagorean theorem, which states that the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the length of the trough, which is 11 ft. So, we can set up the equation as 11^2 = b^2 + b^2, which simplifies to 11^2 = 2b^2. Solving for b, we get b = 7.78 ft.

Now, we can plug in the values of b and V (15 gallons = 3465 cubic inches) into the volume formula. 3465 = (1/2)(7.78)(h), which simplifies to h = 888.36 cubic inches. Since 231 cubic inches is equal to 1 gallon, we can convert the height to gallons by dividing by 231. Therefore, the depth of the water in the trough is approximately 3.84 gallons.

In conclusion, the water depth in the DIY trough is 3.84 gallons. I hope this explanation helped you understand the concept better. Keep practicing and exploring the world of physics!