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Spiraling up/uniform circular motion, combined with constant velocity (Help!)

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cassandralynn
#1
Sep29-10, 08:47 PM
P: 1
1. The problem statement, all variables and given/known data
Please help!! This is my question!

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 3.00m/s .
a)Find the speed of the bird relative to the ground.
b)Find the magnitude of the bird's acceleration.
c)Find the direction of the bird's acceleration.
d)Find the angle between the bird's velocity vector and the horizontal.

2. Relevant equations
I'm not to sure of the equations that I should really use as I am trying to re-learn all the math behind it! My guesses are:
a) a(rad) = v^2/R and stops from there...

3. The attempt at a solution
I have made a diagram of what I think it should look like but thats about as far as my attempt goes... I am in need of some help and advice, My main problem is looking at the question and trying to decide what equation will give me the right answer. Please help!
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fss
#2
Sep29-10, 08:54 PM
P: 1,185
(a) you can find the linear distance the bird travels in one revolution and then divide by the time it takes to get the velocity.

(b) Use the formula you gave as a relevant equation.

(c) In circular motion, where does the acceleration vector point?

(d) You know the linear velocity (vx) and the vertical velocity (vy). If you draw a diagram, it should be apparent that you can find the angle with some simple geometry.

edit: for (b) and (c) you might need to take into account gravity. This means you'll need to do a bit of geometry as well.


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