In problem #s 1 and 2, use the following information. The indicated airspeed S (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures.

The relationship between S and p can be modeled by S=136.4p−−√+4.5.

1. Find the differential pressure when the indicated airspeed is 157 knots.

2. Find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots.

In problem #s 3 and 4, use the following information.

The true airspeed T (in knots) of an airplane can be modeled by T=(1+A50,000) ⋅ S, where A is the altitude (in feet) and S is the indicated airspeed (in knots).

3. Write the equation for true airspeed T in terms of altitude and differential pressure p.

4. A plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet.

Estimate the differential pressure. Explain why you think your estimate is correct.