The airplane, traveling at a constant speed of $50 \mathrm{m} / \mathrm{s}$ is executing a horizontal turn. If the plane is banked at $\theta=15^{\circ},$ when the pilot experiences only a normal force on the seat of the plane, determine the radius of curvature $\rho$ of the turn. Also, what is the normal force of the seat on the pilot if he has a mass of $70 \mathrm{kg}.$