To determine the resulting speed of the bird, we need to combine the bird's velocity with the velocity of the wind.
First, we need to break down the bird's velocity into its horizontal and vertical components. We can find the horizontal component by multiplying the bird's speed by the cosine of the angle between its direction and the east direction.
Horizontal Component = Bird's Speed * cosine(Angle)
In this case, the bird's speed is 30 mph, and the angle is 30 degrees south of east. So we have:
Horizontal Component = 30 mph * cosine(30 degrees) = 30 mph * 0.866 = 25.98 mph (rounded to two decimal places)
The vertical component can be found by multiplying the bird's speed by the sine of the angle between its direction and the east direction.
Vertical Component = Bird's Speed * sine(Angle)
Using the same values as before, we get:
Vertical Component = 30 mph * sine(30 degrees) = 30 mph * 0.5 = 15 mph
Now, we can consider the effect of the wind. The wind is blowing from the northeast to the southwest, which is perpendicular to the bird's flight direction. We can think of the wind's velocity as a vector with a horizontal and vertical component.
The horizontal component of the wind is the same as its speed, which is 10 mph. However, since it's blowing from the northeast, its horizontal component will be negative.
Horizontal Component of Wind = -10 mph
The vertical component of the wind is also -10 mph since it's blowing from the northeast to the southwest.
Vertical Component of Wind = -10 mph
To determine the resulting speed of the bird, we need to add the horizontal and vertical components of the bird's velocity to the horizontal and vertical components of the wind's velocity.
Horizontal Resultant Velocity = Horizontal Component of Bird's Velocity + Horizontal Component of Wind
Vertical Resultant Velocity = Vertical Component of Bird's Velocity + Vertical Component of Wind
In this case, the bird's velocity is solely in the horizontal plane, so the vertical component of the bird's velocity and the vertical component of the wind's velocity are both zero.
Horizontal Resultant Velocity = 25.98 mph + (-10 mph) = 15.98 mph (rounded to two decimal places)
Finally, we can find the resulting speed of the bird by using the Pythagorean theorem:
Resultant Speed = square root((Horizontal Resultant Velocity)^2 + (Vertical Resultant Velocity)^2)
In this case, since the vertical component is zero, the resulting speed simplifies to:
Resultant Speed = square root((15.98 mph)^2 + (0 mph)^2) = square root(255.68 mph^2) = 15.99 mph (rounded to two decimal places)
Therefore, the resulting speed of the bird is approximately 15.99 mph.