Question

Vultures make use of air thermals by spiraling upward on them. Say a particular vulture is spiraling in a radius of 7.00 m and makes one complete turn every 2 s. It is rising vertically at a constant rate of 2 m/s.

a. What is its speed relative to the ground?

b. What is the acceleration?

c. What is the angle between the bird’s velocity vector and the horizontal.

Answer #1

given ,

radius (R) = 7 m

time (T) = 2 s

constant rate ( Vc ) = 2 m/s

a)

Speed = sqrt(Vc^2 + Vab^2) [ Vab = 2*pi*R/T]

= sqrt(Vc^2 + (2*pi*R / T)^2)

= sqrt(2^2 + (2*3.14*7 / 2)^2)

=sqrt(4 + 483.12)

= 22.071 m/s

=======================================

b)

acceleration = 4* (pi)^2 *R / T^2

= 4 * 3.14^2 * 7 / 2^2

= 276.069 / 4

= 69.017 m/s^2

===================================

c)

angle(theta) = tan^-1 ( Vc / Vab) [ Vab = 2*pi*R/T]

=tan^-1(2 / 21.98)

= tan^-1(0.091)

= 5.2 degrees

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