It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 8.00m every 5.00s and rises vertically at a rate of 3.00 m/s .

Find the speed of the bird relative to the ground.

Find the magnitude of the bird's acceleration

Find the direction of the bird's acceleration.

Find the angle between the bird's velocity vector and the horizontal.

Can someone please help with the forumla's?

Please do not keep posting the same question.

I answered previous posting.

Sure! Let's break down the problem step by step.

1. Find the speed of the bird relative to the ground:
To find the speed, we need to consider the circular motion and the upward velocity. The speed of the bird relative to the ground can be found by taking the magnitude of the bird's velocity vector.
The bird completes a circle of radius 8.00m every 5.00s, so the circumference of the circle is 2πr = 2π(8.00m) = 16πm. Since the bird takes 5.00s to complete the circle, the bird's angular speed is ω = 2π/5 rad/s.
The tangential speed of the bird, which is the speed perpendicular to the radial direction, is given by v = rω. So, the bird's tangential speed is (8.00m)(2π/5 rad/s).
Adding the upward velocity of 3.00m/s, the speed of the bird relative to the ground is the magnitude of these vectors combined.

2. Find the magnitude of the bird's acceleration:
The acceleration of the bird can be calculated by the centripetal acceleration due to circular motion. The centripetal acceleration is given by a = v²/r, where v is the tangential speed and r is the radius. So, the magnitude of the bird's acceleration is (v²/r).

3. Find the direction of the bird's acceleration:
The direction of the bird's acceleration is towards the center of the circular path, which is directed radially inward.

4. Find the angle between the bird's velocity vector and the horizontal:
To find the angle, we need to consider the components of the bird's velocity vector. The horizontal component can be determined by multiplying the tangential speed by cosine of the angle. Dividing this by the speed of the bird relative to the ground will give us the cosine of the angle between the bird's velocity vector and the horizontal. Taking the inverse cosine of this value will give us the angle.

By using these formulas, you should be able to find the answers to all the questions. Just plug in the given values for radius, time, and upward velocity to calculate the speed, magnitude of acceleration, direction of acceleration, and the angle between the bird's velocity vector and the horizontal.