It is common to see birds of prey rising upward on thermals. The paths they take

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 8.00 every 5.00 and rises vertically at a rate of 3.00 .

Find the speed of the bird relative to the ground.
I got v=10.5 m/s

Find the magnitude of the bird's acceleration.
a=12.6 m/s^2

Now, this is what I DON'T know how to answer. Please help:
Find the direction of the bird's acceleration (written as degrees above the horizontal)

Thank you so much!

Explanation / Answer

(a)

speed=distance/time.
after 5 seconds, the bird travels a spiral of length 52.45 metres (length of the spiral curve).
speed = 52.45 / 5 = 10.5 m/s.

(b)

Acceleration in vertical direction is 9.8 m/s2   (value of g).

radial acceleration of bird = v2/r = 12.63 m/s2  

(c)

the angle between the velocity

tangential velocity = 0

angular velocity = * r = (2 * pi / 5) * r = 10.05 m/s.

total horizontal velocity = 10.05.

vertical velocity = 3 m/s

angle between resultant and holizontal = tan-1 ( vertical / horizontal ) = tan-1 (3/10.05) = 16.62 degrees.

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