Respuesta :
Answer:
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
Answer:
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
