When a particle is dropped from rest relative to the surface of the earth at a latitude...

When a particle is dropped from rest relative to the surface of the earth at a latitude γ, the initial apparent acceleration is the relative acceleration due to gravity g_rel. The absolute acceleration due to gravity g is directed toward the center of the earth. Derive an expression for grel in terms of g, R, ω, and γ, where R is the radius of the earth treated as a sphere and ω is the constant angular velocity of the earth about the polar axis considered fixed. (Although axes x-y-z are attached to the earth and hence rotate, we may use Eq. 3/50 as long as the particle has no velocity relative to x-y-z). (Hint: Use the first two terms of the binomial expansion for the approximation.)