Air pressure decreases at a rate of 2.5 pascals per kilometer in the eastward direction. In addition, the air pressure is increasing at a constant rate with respect to time everywhere. A ship sailing eastward at 8 km/hour past an island takes barometer readings and records a pressure drop of 30 pascals in 2 hours. Estimate the time rate of change of air pressure on the island. (A pascal is a unit of air pressure.)

The problem tell us that as air pressure decreases with distance, it also increases with time at a constant rate. Therefore, we have to determine in first place, what would be the decrease of air pressure due to distance:

d: total route of the ship in 2 hours

[tex]d=\frac{8km}{h} *2h=16 km[/tex]

D: total decrease of pressure due to distance in 2 hours

[tex]D=16km*\frac{2.5Pa}{km} =40 Pa[/tex]

However, the problem states that the barometer records a pressure drop of 30 pascals in 2 hours. That means, that the rate of air pressure increase due to air, could be determined as follows:

R: time rate of change of air pressure

[tex]R=\frac{40Pa}{2h} -\frac{30Pa}{2h}\\R=\frac{20Pa}{h} -\frac{15Pa}{h}\\R=5 \frac{Pa}{h}[/tex]

Then, despite the decrease of air pressure due to distance, the increase due to time makes lower the drop.