Final answer:
The magnitude of the resultant velocity for the bird flying first at a speed of 10 m/s North East and then flying to the South at a speed of 8 m/s is approximately 16.24 m/s.
Step-by-step explanation:
To find the magnitude of the resultant velocity, we can use vector addition.
The bird flies first at a speed of 10 m/s North East and then flies to the South at a speed of 8 m/s.
These velocities can be represented as vectors.
Since the bird is flying at a speed of 10 m/s North East, the vector representing this velocity can be split into its North and East components.
The North component can be found using trigonometry: sin(45°) * 10 = 7.07 m/s.
The East component can be found using trigonometry: cos(45°) * 10 = 7.07 m/s.
The bird then flies at a speed of 8 m/s to the South.
When an object is moving in the opposite direction, we can consider it as having a negative velocity.
So, the South velocity can be represented as -8 m/s.
To find the resultant velocity, we can add the North and East components to the South velocity.
The North component is 7.07 m/s, the East component is 7.07 m/s, and the South velocity is -8 m/s.
Adding these vectors together, we get:
Resultant velocity = 7.07 m/s North + 7.07 m/s East + (-8 m/s South)
= 7.07 m/s North + 7.07 m/s East - 8 m/s South.
Therefore, the magnitude of the resultant velocity is the square root of the sum of the squares of the North, East, and South velocities:
Magnitude of resultant velocity = sqrt((7.07)^2 + (7.07)^2 + (-8)^2)
= sqrt(99.99 + 99.99 + 64)
= sqrt(263.98)
≈ 16.24 m/s.