An airplane is flying in air with a density of 1.29 kg/m³. A pressure gauge measures the difference in pressure between a point on the nose of the airplane and a point on the fuselage. The pressure on the nose is higher by 60.0 kPa. What is the speed of the plane relative to the air? A) 295 m/s B) 300 m/s C) 305 m/s D) 310 m/s E) 315 m/s

Question

Quizplus · Accepted Answer

The difference between the pressure points can be used to find the dynamic pressure using the Bernoulli's equation:

ΔP = ½ ρ v²

where:
ΔP = difference in pressure
ρ = air density
v = velocity of the airplane relative to the air

Rearranging the equation for v:

v = √(2 ΔP / ρ)

Substituting the given values:

v = √(2 x 60.0 x 10³ / 1.29) = 305 m/s

Therefore, the speed of the plane relative to the air is 305 m/s, which corresponds to answer C.

An Airplane Is Flying in Air with a Density of 1.29