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