The pressure P at the bottom of a swimming pool varies directly as depth of water. If the pressure is 125 paacal when the water is 2m deep ,find the pressure when it 4.5 meters deep.
That is basically wrong because you are ignoring the atmospheric pressure of the air above the water so the variation is NOT DIRECT
p = k x
but linear
p = patmosphere + k x
but if we ignore the physics and do it the way the math people want you to do it then
P at 4.5 m = 125 *4.5/2 = 281
because the gravity falls asleep in the World Series game and I have been there since before I'll see if you want me to do it for the day before yesterday was the last one was there
To solve this problem, we can set up a proportion using the given information.
According to the problem, the pressure P at the bottom of the swimming pool varies directly as the depth of water. This can be represented mathematically as:
P ∝ d
Where P is the pressure and d is the depth of water.
We are given that when the water depth is 2 meters, the pressure is 125 pascals. We can use this information to find the constant of variation (k) by substituting these values into the equation:
125 = k * 2
To find k, we divide both sides of the equation by 2:
k = 125/2 = 62.5
Now that we have the value of k, we can use it to find the pressure when the water depth is 4.5 meters. Plugging this into the equation:
P = k * d
P = 62.5 * 4.5
P = 281.25
Therefore, when the water depth is 4.5 meters, the pressure at the bottom of the swimming pool is 281.25 pascals.
To find the pressure when the water is 4.5 meters deep, we can use the concept of direct variation.
Direct variation states that when two variables are directly proportional, their ratio remains constant. In this case, the pressure (P) is directly proportional to the depth of water (d).
We can represent this relationship as P = kd, where k is the constant of variation.
To find the value of k, we can use the given information that the pressure is 125 Pascal when the water is 2 meters deep. Plugging these values into the equation, we get:
125 = k * 2
To solve for k, divide both sides of the equation by 2:
k = 125 / 2
k = 62.5
Now that we know the value of k, we can substitute it back into the equation P = kd to find the pressure when the water is 4.5 meters deep:
P = 62.5 * 4.5
P = 281.25
Therefore, the pressure at the bottom of the swimming pool when the water is 4.5 meters deep is 281.25 Pascal.