Final answer:
The robin's speed relative to the ground is 13.47 m/s.
Step-by-step explanation:
The robin's speed relative to the ground can be found using vector addition. We can break down the robin's velocity into its northward and eastward components using trigonometry. The northward component of the robin's velocity is 12 m/s, and the eastward component of the air's velocity is 6.1 m/s. To find the resultant velocity, we can use the Pythagorean theorem. Since the robins' velocity is due north and the air's velocity is due east, the resultant velocity will form a right triangle with sides of 12 m/s and 6.1 m/s. Using the Pythagorean theorem, we can solve for the hypotenuse, which represents the robin's speed relative to the ground.
By substituting the given values into the Pythagorean theorem equation c^2 = a^2 + b^2, where a = 12 m/s and b = 6.1 m/s, we get:
c^2 = (12 m/s)^2 + (6.1 m/s)^2
c^2 = 144 m^2/s^2 + 37.21 m^2/s^2
c^2 = 181.21 m^2/s^2
c = √(181.21 m^2/s^2) = 13.47 m/s
Therefore, the robin's speed relative to the ground is approximately 13.47 m/s.