The intensity I of light bulb measured in watts per square meter (w/m^2), varies inversely as the square of the distance d from the light bulb . . suppose I is 45 w/m^2 when the distance is 5 m . find the intensity when the distance from the light bulb is 7 m away
I = k(1/d^2)
when I = 45, d = 5
45 = k/25
k =1125
so I = 1125/d^2
when d = 7
I = 1125/49 = appr 22.96
22.95918367
Well, determining the intensity of light using the inverse square law can be illuminating... or not so illuminating, in this case.
Let's start with what we know. The intensity I varies inversely with the square of the distance d. So we can set up the equation: I1 × d1^2 = I2 × d2^2, where I1 is the initial intensity, d1 is the initial distance, I2 is the final intensity, and d2 is the final distance.
Now let's plug in the values we have. We know that I1 is 45 w/m^2 and d1 is 5 m. We want to find I2 when d2 is 7 m.
So we have: 45 × 5^2 = I2 × 7^2.
Now it's just a matter of solving for I2. Bear with me, this might get a little intense...
First, let's simplify 5^2 to 25, and 7^2 to 49. That gives us: 45 × 25 = I2 × 49.
Now let's solve for I2. Divide both sides of the equation by 49: (45 × 25) ÷ 49 = I2.
Calculating that gives us: I2 ≈ 22.96 w/m^2.
So, when the distance from the light bulb is 7 m away, the intensity is approximately 22.96 w/m^2. A bit dimmer, but hey, still bright enough to light up your day!
To find the intensity when the distance from the light bulb is 7 m away, we can use the inverse square relationship between intensity and distance.
Let's denote the intensity by I and the distance by d. According to the problem, the intensity I varies inversely as the square of the distance d. This can be expressed mathematically as:
I ∝ 1/d^2
We are given the following information: when the distance is 5 m, the intensity is 45 w/m^2. Using this information, we can set up a proportion:
I1/d1^2 = I2/d2^2
Substituting the values given: I1 = 45 w/m^2, d1 = 5 m, and d2 = 7 m, we get:
45/5^2 = I2/7^2
Simplifying the equation gives us:
45/25 = I2/49
To solve for I2, we can cross-multiply:
45 * 49 = 25 * I2
2,205 = 25 * I2
Dividing both sides by 25:
I2 = 2,205/25
I2 = 88.2 w/m^2
Therefore, the intensity when the distance from the light bulb is 7 m away is approximately 88.2 w/m^2.