Question

A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 12 m/s. A wise elder duck realizes that the solution is to fly at an angle to the wind. If the ducks can fly at 16 m/s relative to the air, in what direction should they head in order to move directly south?

Answer 1

The angle taken by the ducks will be 48.6 degrees.

Step-by-step explanation:

As the opposing speed is coming from the west direction with speed of 12 m/s. And as one elder duck found that they can fly with speed of 16 m/s by flying at an angle to the wind. Then we can determine the resultant vector sum of the velocity to find the angle. Since here two vector velocities are acting on the bird, the sum of them will be equal to the resultant velocity.

So vector velocity of duck moving by wind + Vector velocity of wind = Resultant velocity.

The velocity components for duck moving by wind is 12 i and the velocity component for wind is -16 sin θ i - 16 cos θ j. The resultant velocity will be having the component of -vj.

So, 12 i -16 sin θ i - 16 cos θ j = - v j

Equating the components we get,

12-16 sin θ = 0

sin θ =
`(12)/(16)`

θ = 48. 6 degrees.

So the angle taken by the ducks will be 48.6 degrees.