# Homework Help: Time rate of change of air pressure

1. Oct 9, 2014

### BondKing

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 10 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.)

What is time rate of change of air pressure?

Attempt:

Basically tried everything possible

10 x 2 = 20 km

30 Pa / 2 hrs = 15 Pa / hr

2.5 Pa x 20 km = 50 Pa

2. Oct 9, 2014

### pasmith

This is an exercise in using the multivariate chain rule in the form $$\frac{dp}{dt} = \frac{\partial p}{\partial t} + \frac{\partial p}{\partial x}\frac{dx}{dt}$$ where $x(t)$ is the position of the ship. You are trying to find $\frac{\partial p}{\partial t}$ which is stated to be constant.

3. Oct 9, 2014

### BondKing

-15 = ∂p/∂t + (-2.5)(10) ?
Is the unit for the answer Pa/hr?

4. Oct 10, 2014

Yes