To calculate the resultant velocity of the swallows, we need to consider both their constant speed and the effect of the wind.
Let's denote the velocity of the swallows as Vswallows, which is 20 km/h at an angle of 21° west of north.
The wind is blowing at a speed of 6 km/h from the southwest direction. Southwest is at an angle of 225° (180° + 45°) from north.
Let's represent the velocity of the wind as Vwind, which is 6 km/h at an angle of 225°.
Now, to calculate the resultant velocity (Vresultant) of the swallows, we can use the law of cosines:
Vresultant = sqrt((Vswallows)^2 + (Vwind)^2 + 2 * Vswallows * Vwind * cos(θ))
where θ is the angle between the velocities of the swallows and the wind. In this case, θ = 180° - 21° = 159°.
Plugging in the values:
Vresultant = sqrt((20)^2 + (6)^2 + 2 * 20 * 6 * cos(159°))
Vresultant = sqrt(400 + 36 + 240 * cos(159°))
Vresultant = sqrt(436 + 240 * cos(159°))
Now, we can calculate the value of Vresultant.
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 their resultant velocity.
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