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

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get

the body's situation won't change the forces are equal opposit and on the same body