an american bald eagle heads south at 3.2 m/s, but encounters a wind blowing from the east at.97 m/s by how many degrees will she be blown off course?
α = arctan(0.97/3.2)=16.86°
To determine the number of degrees the American bald eagle will be blown off course, we need to calculate the angle between the bird's heading direction (south) and the resultant direction after accounting for the effect of the wind.
To do this, we can use trigonometry, specifically the tangent function. The tangent of an angle can be calculated by dividing the length of the side opposite the angle by the length of the side adjacent to the angle.
In this context, the side opposite the angle we want to find is the eastward component of the wind's force (0.97 m/s), and the side adjacent to the angle is the southward component of the bird's velocity (3.2 m/s).
Let's calculate the tangent of the angle θ:
tan(θ) = opposite / adjacent
tan(θ) = 0.97 / 3.2
Now, we can find the angle θ by taking the inverse tangent (or arctan) of the ratio we just calculated:
θ = arctan(0.97 / 3.2)
Using a calculator or a math library function, we find:
θ ≈ 16.0805 degrees
Therefore, the American bald eagle will be blown off course by approximately 16.0805 degrees due to the wind.