Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. The one goose is flying at 100 km/h relative to the air but a 50 km/h wind is blowing from west to east. Part A
At what angle relative to the north-south direction should this bird head to travel directly southward relative to the ground?Part B
How long will it take the goose to cover a ground distance of 550 km from north to south?

a. The angle at which the goose must be travelling relative to the north-south direction is 210°

b. 6.35 h

Explanation:

Part A

At what angle relative to the north-south direction should this bird head to travel directly southward relative to the ground

Adding vectorially v₁ = v₂ + v₃ where v₁ = velocity of goose relative to ground, v₂ = velocity of wind relative to ground and v₃ = velocity of goose relative to air.

So  v₁ = √(100² - 50²) = √(10000 - 2500) = √7500 =  86.6 km/h

The angle between the relative velocity of goose to wind and goose to ground is cosθ = velocity of goose to ground/velocity of goose relative to wind = 86.6km/h/100km/h = 0.8660

θ = cos⁻¹0.8660 = 30°

So, the angle at which the goose must be travelling relative to the north-south direction is 180° + 30° = 210°

Part B

How long will it take the goose to cover a ground distance of 550 km from north to south?

Since the velocity of goose relative to ground = 86.6 km/h,

Since time = distance/speed = 550 km/86.6 km/h = 6.35 h