A Being 747 jumbo jet maintains an airspeed of 650 miles per

A Being 747 jumbo jet maintains an airspeed of 650 miles per hour in a southwesterly direction. The velocity of the jet stream is a constant 40 miles per hour from the west. Find the actual speed and direction of the aircraft. What is the actual speed of the aircraft? miles per hour

Solution

let actual speed be -xi^ - yj^

now => (-x + 40)i^ - yj^ = -650/sqrt(2) (i^ + j^)

x = 499.62 mile/hr , y = 459.62 mile/hr

actual speed = sqrt(499.62² + 459.62²) = 678.874 mile/hr

direction , tan(theta) = 459.62/499.62 => theta = 42.61 degree south of west