The pressure p at the bottom of swimming pool varies directly as the depth d of the water. If the pressure is 125 Pascal when the water is 2 meters deep, find the pressure when it is 4.5 meters deep.
Equation➡ p=kd
125=k(2)
125/2=2k/2
125/2=k or K=125/2
P=(125/2)(4.5)
P=281.25 ⬅Answer
214.8
Well, isn't that a deep question! Let's dive into it, shall we?
We know that pressure varies directly with depth. So, if the pressure is 125 Pascal at a depth of 2 meters, we can set up a direct variation equation: p = kd, where k is the constant of variation.
To find the value of k, we can plug in the given values: 125 = k * 2. Solving for k, we get k = 125/2 = 62.5.
Now we can use this value of k to find the pressure when the water is 4.5 meters deep. Plugging the values into our equation, we get p = 62.5 * 4.5. Doing the math, we find that the pressure is 281.25 Pascal.
So, when the water depth reaches 4.5 meters, the pressure at the bottom of the swimming pool will be 281.25 Pascal. Just be careful not to get too deep, you might pop like a party balloon!
To find the pressure when the water is 4.5 meters deep, we can use the concept of direct variation.
Direct variation means that two variables are proportional to each other. In this case, the pressure and the depth of the water are directly proportional.
We can set up a proportion to solve for the unknown pressure.
Let's use the following proportion:
p1/d1 = p2/d2
where:
- p1 is the initial pressure (125 Pascal)
- d1 is the initial depth (2 meters)
- p2 is the unknown pressure (to be determined)
- d2 is the desired depth (4.5 meters)
Substituting the given values:
125/2 = p2/4.5
To find p2, we can cross multiply and solve for it:
125 * 4.5 = 2 * p2
562.5 = 2 * p2
Dividing both sides by 2:
562.5/2 = p2
281.25 = p2
Therefore, the pressure when the water is 4.5 meters deep is 281.25 Pascal.
To find the pressure when the water is 4.5 meters deep, we can set up a proportion based on the direct variation relationship between pressure and depth.
1. Begin by writing the direct variation equation: p = kd, where p is the pressure, d is the depth, and k is the constant of variation.
2. To solve for k, we can substitute the given values into the equation. We know that when the depth is 2 meters, the pressure is 125 Pascal. Substituting these values into the equation gives us: 125 = k * 2.
3. Solve the equation for k by dividing both sides by 2: k = 125 / 2 = 62.5.
4. Now that we have the value of k, we can use it to find the pressure when the depth is 4.5 meters. We substitute 4.5 for d in the equation: p = 62.5 * 4.5.
5. Calculate the pressure: p = 62.5 * 4.5 = 281.25 Pascal.
Therefore, the pressure when the water is 4.5 meters deep is 281.25 Pascal.