# Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to

Question

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?

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1 year 2021-09-05T14:06:59+00:00 2 Answers 82 views 0

θ = 30°   ( West of south )

t = 6.35 hrs

Explanation:

Given:

The velocity of goose relative to air v_B/A = 100 km/h

– The velocity of wind v_w = 50 km/h

– The angle relative to ground θ

– Distance traveled from North-South d = 550 km

Find:

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?

Solution:

– We want the bird to fly with speed v_B/A = 100 km/h with an angle θ relative to ground so that the bird fly due south relative to ground. (See Attachment)

– From the figure we got by using trigonometric ratios:

sin(θ) = v_w / v_B/A

sin(θ) = 50/100

θ = 30°   ( West of south )

The bird will have only north-south velocity relative to the earth v_B/G:

v_B/G = v_B/A*cos(θ)

v_B/G = 100*cos(30)

v_B/G = 86.603 km/h

– Applying distance time relationship we have:

t = d / v_B/G

t = 550 / 86.603

t = 6.35 hrs

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