Relative Circular Speed given radius and time

In summary, the speed of the bird relative to the ground can be found by adding the horizontal and vertical components of its velocity, which are calculated using the equations for velocity and circumference. This gives a total speed of 7.5398m/s for the bird's circular motion and 3m/s for its rising velocity.
  • #1
brh8447
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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!
 
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  • #2
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.
 
  • #3
Thanks TSny! I was confused with what exactly relative motion encompassed when considering what the motion was relative to when working with 3D vectors
 

1. What is relative circular speed?

Relative circular speed refers to the speed at which an object is moving in a circular path relative to another object or reference point.

2. How is relative circular speed calculated?

Relative circular speed is calculated by dividing the circumference of the circle by the time it takes for the object to complete one full rotation.

3. What is the relationship between radius and relative circular speed?

The relationship between radius and relative circular speed is inversely proportional. This means that as the radius increases, the relative circular speed decreases and vice versa.

4. How does time affect relative circular speed?

Time does not have a direct effect on relative circular speed. However, as time increases, the distance traveled in a circular path also increases, resulting in a higher relative circular speed.

5. Can relative circular speed be negative?

No, relative circular speed cannot be negative. It is a measure of the magnitude of the speed and therefore is always positive.

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