# Uniform Motion

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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.

• Uniform Motion - ,

The vertical motion and the horizontal motion are decoupled. The vertical velocity is v = 3 m/s and the vertical acceleration is 0 m/s^2
In the horizontal plane the speed is u = 2 pi r/T = 2 pi (8/5) = 10 m/s
and the acceleration is centripetal = v^2/r = 12.6 m/s^2 toward the center of the spiral
So the speed relative to ground is:
s = sqrt(u^2+v^2)
The acceleraation is all inward in the horizontal plane and is 12.6 m/s^2
tan theta = v/u = 3/10