Question

The atmospheric pressure P on a balloon or in aircraft decreases with increasing height . This pressure measured in Millimeters of mercury , is related to the height H (in kilometers) above sea level by the formula p=760e ^ -0.145h. See photo for formula and answer following questions.
A.) find the height of an aircraft if the atmospheric pressure is 344 millimeters of Mercury. (Round to two decimal places)
B.) find the height of a mountain if the atmospheric pressure is 622 millimeters of mercury.
(Round to two decimal places)

Answer 1

Answer:

(A)   5.47 km

(B)   1.38 km

Step-by-step explanation:

The relationship between Pressure (mmHg) and Height (km) is given by the equation below:

p =760 e⁻ 0.145h----------------------------------------------------- (1)

(a) The height of the aircraft can be calculated by making 'h' the subject of equation (1)

In (p/760) = -0.145 h

h = -In (p/760) /0.145

h= In (760/p)/ 0.145------------------------------------------------- (2)

For the aircraft, p =344 mmHg; substituting into (2)

h = In (760/344)/0.145

   = 0.7926/0.145

   = 5.4662 km

   ≈ 5.47 km

(b) p= 622 mmHg at the mountain top. Substituting into equation  (2) we have:

h = In (760/622)/0.145

  = 0.2003 / 0.145

  =  1.3813 km

  ≈  1.38 km