Q. 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 x m every t s and rises vertically at a rate of y m/s.
Find the speed of the bird relative to the ground.
Is the speed of the birdie equals to [2(pi)x] / t
Vertical velocity =y
Horizontal velocity = r * angular velocity = x * (2π/t) = 2πx/t
So, speed relative to ground = sqrt {(vertical speed)² + (hort speed)²}