Relative Circular Speed given radius and time

[brh8447]

Homework Statement

What is the speed of the object (a bird) relative to the ground?
We are given that a bird is flying in a spiraling path and rising on a thermal, making circles with a radius of 6m every 5s and rising strait up at a velocity of 3m/s.

Homework Equations

V=d/t
C=2πr=d

The Attempt at a Solution

My attempt at this problem was to solve the total distance the bird travels around the circle (this is our circumference (d))

C=d=2π(6m)=37.699m

Then use the general equation for velocity to find the velocity the bird must have in order to go this distance over the time of 5s.

V=37.699m/5s=7.5398m/s

This answer was wrong. I'm unsure of what velocity this gives me. I'm assuming that since it's circular motion, this is the vector that is the tangent of the circle. There is also the issue of its relativity to the ground. Since the birds motion in its circular path is in the x/y coordinate grid (the velocity upward being z) and I am considering the x/y plane to be the ground, where am I going wrong? Thanks so much for whoever is able to help!

 

[TSny]

You have found the magnitude of the horizontal component of the velocity (tangent to the circular motion if the bird were not rising). To this, you need to add (vectorially) the vertical component.

 

[brh8447]

Thanks TSny! I was confused with what exactly relative motion encompassed when considering what the motion was relative to when working with 3D vectors