Consider a hemisphere with a flat base in a hypersonic flow at \(0^{\circ}\) angle of attack (the hemispherical portion faces into the flow). Assuming that the base pressure is equal to free-stream static pressure, use modified newtonian theory to derive an expression for the drag coefficient \(C_{D}=D / q_{\infty} \pi R^{2}\) as a function of \(C_{p_{\max }}\).