3. Find the air temperature if sound travels 205 m in 0.6 seconds

Known :

S = 205 m

t = 0.6 s

Solution :

Sound speed

v = S/t

v = (205 m)/(0.6 s)

v = 341.67 m/s

Air Temperature

v² = γRT

(341.67 m/s)² = (1.4)(286 m²/s²·K)(T)

T = 291.5 K

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