In a movie, Tarzan evades his captors by hiding under water for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is -85 mm-Hg, calculate the deepest he could have been.
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This is Giancoli Answers with Mr. Dychko. So the pressure that the Tarzan's lungs have to deal with here are on the one hand, pressure due to the water pushing air out of the lungs and that's gonna be the atmospheric pressure applied to the surface of the water plus the additional pressure due to this water that's between the top of his chest and the surface of the water so we'll call that ΔP and then pushing air down into his lungs through the reed is atmospheric pressure. So what the lungs have to do is basically make the pressure's equal between the outside and inside of the lungs and when it's just barely equal that's when he's able to breathe. So when the pressure inside the lung is slightly less than the water pressure on the outside of the lungs that's when he's able to breathe. So we have P a plus ΔP equaling P a and so the P a's cancel on both sides and we are just left with ΔP which is what we need to find. So ΔP the pressure due to just the column of water there is the density of water times g times the height of the water column and that's something we can rearrange by dividing both sides by ρg to solve for Δh. So that's the maximum pressure is that's the maximum water column pressure that his lungs can tolerate 85 millimeters of mercury which we convert into pascals by multiplying by 133 pascals per millimeter of mercury then divide by the density of water— 1.00 times 10 to the 3 kilograms per cubic meter— times by 9.8 newtons per kilogram and that gives 1.2 meters would be the maximum depth that Tarzan could stay at and still breathe through this reed.
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