An American bald eagle heads south at

5.5 m/s, but encounters a wind blowing from
the east at 1.9 m/s.
By how many degrees will she be blown o�
course?

what is arc tan (1.9/5.5)? that is the degrees W of S.

To determine by how many degrees the eagle will be blown off course, we need to find the direction of the resulting velocity vector. We can use vector addition to solve this problem.

Let's break down the velocities into their components. The eagle's velocity can be split into a north-south component (y-component) and an east-west component (x-component). The wind velocity can also be split into these two components.

Given:
Eagle's velocity (v1) = 5.5 m/s south
Wind velocity (v2) = 1.9 m/s east

Now, we can find the x and y components of the resulting velocity.

x-component of resulting velocity (vx):
vx = v2 = 1.9 m/s (since the wind only blows in the east-west direction)

y-component of resulting velocity (vy):
vy = v1 = 5.5 m/s (since the eagle is heading south)

Next, we can find the magnitude and direction of the resulting velocity using the Pythagorean theorem and trigonometry.

Magnitude of resulting velocity (v_result):
v_result = √(vx^2 + vy^2)
v_result = √((1.9)^2 + (5.5)^2)
v_result ≈ 5.803 m/s

To find the direction, we can use trigonometry.

Direction (θ):
θ = tan^(-1)(vy/vx)
θ = tan^(-1)(5.5/1.9)
θ ≈ 71.29°

Therefore, the eagle will be blown off course by approximately 71.29 degrees.