Let's denote the initial amount of wood on the fire as W1 and the initial distance from the fire as D1. We'll also call the initial heat experienced by the hiker as H1.
According to the given information, we have the following proportionalities:
Heat ∝ Wood
Heat ∝ 1/Distance^3
So we can write the equation as follows:
H1 ∝ W1 / D1^3
Now, let's say someone doubles the amount of wood burning, the new amount of wood on the fire is 2W1. Let's call the new distance from the fire as D2.
For the heat to remain the same, we can set up a new equation:
H1 = (2W1) / D2^3
We want to find D2, the new distance from the fire. To do so, we can rearrange the equation:
D2^3 = (2W1) / H1
D2 = (2W1 / H1)^(1/3)
Now, we substitute the given values:
H1 = 18ft (as given)
W1 = amount of wood on fire
D1 = 18ft (as given)
Since we don't know the actual amount of wood on the fire, we'll denote it as W1.
D2 = (2W1 / 18)^(1/3)
D2 = (2W1)^(1/3) / 18^(1/3)
D2 = (2)^(1/3) * W1^(1/3) / (18^(1/3))
D2 = (2)^(1/3) * W1^(1/3) / 2
D2 = (2)^(1/3) * (W1/2)^(1/3)
Thus, if the person doubles the amount of wood burning and wants to feel the same heat as before, they would have to be approximately (2)^(1/3) ≈ 1.26 times as far from the fire.
Therefore, if the initial distance from the fire was 18ft, the person would have to be approximately 1.26 * 18ft ≈ 22.7ft from the fire to feel the same heat as before.
The heat experienced by a hiker at a campfire is proportional to the amount of wood on the fire and inversely proportional to the cube of his distance from the fire if the hiker is 18ft from the fire and someone doubles the amount of wood burning how far from the fire would he have to be so that he feels the same heat as before?(round your answer to one decimal place) in ft?
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