To calculate the distance travelled after 12 hours of flight, we first need to break down the velocities of the swallows and the wind into their horizontal and vertical components.
The swallows are flying at a constant speed of 20 km/h in a direction 21° west of north. This can be broken down into horizontal and vertical components as follows:
Horizontal component: 20 km/h * cos(21°) = 18.55 km/h
Vertical component: 20 km/h * sin(21°) = 7.06 km/h
The wind is blowing at a speed of 6 km/h from the southwest. This can be broken down into horizontal and vertical components as follows:
Horizontal component: 6 km/h * cos(225°) = -4.24 km/h
Vertical component: 6 km/h * sin(225°) = -4.24 km/h
Now, we can calculate the total horizontal and vertical velocities of the swallows:
Total horizontal velocity = 18.55 km/h - 4.24 km/h = 14.31 km/h
Total vertical velocity = 7.06 km/h - 4.24 km/h = 2.82 km/h
Now, we can calculate the total distance travelled after 12 hours using the Pythagorean theorem:
Distance = sqrt((14.31 km/h)^2 + (2.82 km/h)^2) * 12 hours
Distance = sqrt(204.08 km^2 + 7.97 km^2) * 12 hours
Distance = sqrt(212.05 km^2) * 12 hours
Distance = 14.56 km/h * 12 hours
Distance = 174.67 km
Therefore, the distance travelled after 12 hours of flight is 174.67 km.
As winter approaches, a flock of swallows departs from South Africa for the north. Using their internal magnetic orientation system, they set their course for 21° west of north. They fly at a constant speed of 20 km/h but a 6-km/h wind from the southwest steers them off course. 3.1 Calculate the distance travelled after 12 hours of flight.
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