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 6.7 m/s relative to the ground. Part A What is the robin's speed relative to the ground?

Answer 1

Here it is given that speed of migrating Robin is 12 m/s relative to air

so we can say that

`\vec v_(ra) = 12 m/s` North

so it will be

Let North direction is along Y axis and East direction is along X axis

`\vec v_(ra) = 12\hat j`

also it is given that speed of air is 6.7 m/s relative to ground

`\vec v_a = 6.7 \hat i`

now as we know by the concept of relative motion

`\vec v_(ab) = \vec v_a - \vec v_b`

`\vec v_(ra) = \vec v_r  - \vec v_a`

now by rearranging the terms

`\vec v_r = \vec v_(ra) + \vec v_a`

`\vec v_r = 12 \hat j + 6.7 \hat i`

now we need to find the speed of Robin which means we need to find the magnitude of its velocity which we found above

So here we will say

`v_r = √(12^2 + 6.7^2)`

`v_r = 13.7 m/s`

so the net speed of Robin with respect to ground will be 13.7 m/s