A Boeing 747 jumbo jet maintains an airspeed of 800 miles pe

A Boeing 747 jumbo jet maintains an airspeed of 800 miles per hour in a southwesterly direction. The velocity of the jet stream is a constant 80 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 (Do not round until the final answer. Then round to the nearest tenth as needed.)

Solution

The Boeing 747 jumbo jet is in southwesterly direction. It means its in third quardrant therefore the angle is 180+45=225 degree

Reultant vector representing jet is 800 cos 225 i + 800 sin 225 j

Vector representing wind=80 i

Resultant vector of the two vectors= 800 cos 225i + 800 sin 225 j + 80 i=-565.7 i + -565.7j +80i

                                                                                                                = -485.7i - 565.7j

Magnitude= sqrt(-485.7²+565.7²) = sqrt(555920.98)= 745.6mi

tan theta=y/x =- 565.7/-485.7

theta= 49.35 degree