Calculate ground speed of plane.

Question

A plane is heading due west: its nose points towards the west direction, but its trajectory on the ground deviates from the west direction due to a sideways component of the wind. The plane is also climbing at the rate of 120 km/h (height increase per unit time). If the plane's airspeed is 480 km/h and there is a wind blowing 80 km/h to the northwest, what is the ground speed of the plane? please answer in exact values or within 4 decimals places, thank you

Answer 1

The problem can be solved by applying vector addition because we can ignore plane climbing in ground speed calculation.

In vector form Plane speed is -480i + 0j and wind speed is (-80/sq. root 2)i + (80/sq. root 2)j

Vector notation wind speed is -56.5685 i + 56.5685j

To find ground speed add vectors. -480i -56.5685i + 56.5685j = -536.5685i + 56.5685j

The magnitude of ground speed [ (-536.5685)^2 + (56.5685)^2]^(1/2) = 539.5422 km/hr

The direction of ground speed is arc tan (56.5685/536.5685) = 0.6368 degrees north of west.

Answer 2