Question

A migrating robin flies due north with a speed of 12 m/s relative to the air. The air moves due east with a speed of 6.8 m/s relative to the ground.

Answer 1

I'm assuming the question is what is the robin's speed relative to to the ground...

Create an equation that describes its relative motion.

rVg = rVa + aVg

Substitute values.

rVg = 12 m/s [N] + 6.8 m/s [E]

Use vector addition.

| rVg | = √ | rVa |² + | aVg |²

| rVg | = √ 144 m²/s² + 46.24 m²/s²

| rVg | = √ 190.24 m²/s²

| rVg | = 13.78 m/s

Find direction.

tanФ = aVg / rVa

tanФ = 6.8 m/s / 12 m/s

Ф = 29°

Therefore, the velocity of the robin relative to the ground is 14 m/s [N29°E]