Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. The ind

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Airplane speeds are measured in three differentways: (1) indicated speed, (2) true speed, and (3)ground speed. The indicatedairspeed is the airspeed given by an instrumentcalled an airspeed indicator. A plane’s indicated airspeed isdifferent from its true airspeed because the indicator is affectedby temperature changes and different altitudes of air pressure. The true airspeed is the speed ofthe airplane relative to the wind. Groundspeed is the speed of the airplane relative to theground. For example, a plane flying at a trueairspeed of 150knots into a headwind of 25knots will have a ground speedof 125 knots.
The problems below referto static and dynamicpressure. Staticpressure is used when a body is in motion or at restat a constant speed and direction. Dynamic pressure is used when a body inmotion changes speed or direction or both. A gauge comparesthese pressures, giving pilots an indicated airspeed.
In problem #s 1 and 2, use thefollowing information.
The indicatedairspeed S (in knots)of an airplane is given by an airspeed indicator that measures thedifference p (in inchesof mercury) between the static and dynamic pressures.
The relationshipbetween S and p canbe modeled by {"version":"1.1","math":"<mathstyle="font-family:Tahoma"xmlns="http://www.w3.org/1998/Math/MathML"><ms ... ><mrow><mi mathvariant="bold-italic"mathcolor="#00007F">S</mi><mo mathvariant="bold"mathcolor="#00007F">=</mo><mn mathvariant="bold"mathcolor="#00007F">136</mn><mo mathvariant="bold"mathcolor="#00007F">.</mo><mn mathvariant="bold"mathcolor="#00007F">4</mn><msqrtmathcolor="#00007F"><mimathvariant="bold">p</mi></msqrt><momathvariant="bold" mathcolor="#00007F">+</mo><mnmathvariant="bold" mathcolor="#00007F">4</mn><momathvariant="bold" mathcolor="#00007F">.</mo><mnmathvariant="bold"mathcolor="#00007F">5</mn></mrow></mstyle></math>"}.
1. Find the differential pressure when the indicatedairspeed is {"version":"1.1","math":"<mathstyle="font-family:Tahoma"xmlns="http://www.w3.org/1998/Math/MathML"><ms ... ><mrow><mn mathvariant="bold"mathcolor="#00007F">157</mn><mo mathvariant="bold"mathcolor="#00007F"> </mo><mimathvariant="bold-italic" mathcolor="#00007F">k</mi><mimathvariant="bold-italic" mathcolor="#00007F">n</mi><mimathvariant="bold-italic" mathcolor="#00007F">o</mi><mimathvariant="bold-italic" mathcolor="#00007F">t</mi><mimathvariant="bold-italic"mathcolor="#00007F">s</mi></mrow></mstyle></math>"}.
2. Find the change in the differential pressure of anairplane that was travelingat {"version":"1.1","math":"<mathstyle="font-family:Tahoma"xmlns="http://www.w3.org/1998/Math/MathML"><ms ... ><mrow><mn mathvariant="bold"mathcolor="#00007F">218</mn><mo mathvariant="bold"mathcolor="#00007F"> </mo><mimathvariant="bold-italic" mathcolor="#00007F">k</mi><mimathvariant="bold-italic" mathcolor="#00007F">n</mi><mimathvariant="bold-italic" mathcolor="#00007F">o</mi><mimathvariant="bold-italic" mathcolor="#00007F">t</mi><mimathvariant="bold-italic"mathcolor="#00007F">s</mi></mrow></mstyle></math>"} andslowed down to{"version":"1.1","math":"<mathstyle="font-family:Tahoma"xmlns="http://www.w3.org/1998/Math/MathML"><ms ... ><mrow><mn mathvariant="bold"mathcolor="#00007F">195</mn><mo mathvariant="bold"mathcolor="#00007F"> </mo><mimathvariant="bold-italic" mathcolor="#00007F">k</mi><mimathvariant="bold-italic" mathcolor="#00007F">n</mi><mimathvariant="bold-italic" mathcolor="#00007F">o</mi><mimathvariant="bold-italic" mathcolor="#00007F">t</mi><mimathvariant="bold-italic"mathcolor="#00007F">s</mi></mrow></mstyle></math>"}.
In problem #s 3 and 4, use the followinginformation.
The trueairspeed T (inknots) of an airplane can be modeledby {"version":"1.1","math":"<math style="font-family:stix"xmlns="http://www.w3.org/1998/Math/MathML"><ms ... "24px"><mi mathvariant="bold-italic"mathcolor="#191919">T</mi><mo mathvariant="bold"mathcolor="#191919">=</mo><mfencedmathcolor="#191919"><mrow><mnmathvariant="bold">1</mn><momathvariant="bold">+</mo><mfrac><mimathvariant="bold">A</mi><mrow><mnmathvariant="bold">50</mn><momathvariant="bold">,</mo><mnmathvariant="bold">000</mn></mrow></mfrac></mrow></mfenced><momathvariant="bold"mathcolor="#191919"> </mo><momathvariant="bold"mathcolor="#191919">·</mo><momathvariant="bold"mathcolor="#191919"> </mo><mimathvariant="bold-italic"mathcolor="#191919">S</mi></mstyle></math>"}, where A isthe altitude (in feet)and S is the indicated airspeed(in knots).
3. Write the equation for trueairspeed T in terms of altitudeand differential pressure p.
4. A plane is flying with a true airspeed of 280knots at an altitude of 20,000 feet.
Estimate the differential pressure. Explain why you thinkyour estimate is correct.