An airplane is cruising at an altitude of several kilometers. The pressure outside the craft is 0.258 atm within the passenger compartment the pressure is 1.00 atm and the temperature is 20∘C. The density of air is 1.20 kg/m3 at 20∘C and 1 atm of pressure. A small leak occurs in one of the window seals in the passenger compartment. Model the air as an ideal fluid to find the speed of the stream of air flowing through the leak.

The speed of the stream of air flowing through the leak is 340.754 m/sec

Explanation:

Carefully applying the Bernoulli's equation the speed of the leak can be obtained. The attached images show step by step explanation of the question, while applying the Bernoulli's equation;

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west