Required information The given figure shows the forces exerted on a hot air balloon system. Formulate the drag force as where Pa- air density (kg/m3). v velocity (m/s), A- projected frontal area (m2), and Cd the dimensionless drag coefficient(0.47 for a sphere). Note also that the total mass of the balloon consists of two components. where mG= the mass of the gas inside the expanded balloon (kg) and mp-the mass of the payload (basket, passengers, and the unexpanded balloon-265 kg. Assume that the ideal gas law holds (P= pR7, that the balloon is a perfect sphere with a diameter of 17.3 m, and that the heated air inside the envelope is at roughly the same pressure as the outside air. The parameters are as follows. normal atmospheric pressure P 101,300 Pa, the gas constant for dry air R- 287 joules/kg K, the air inside the balloon is heated to an average temperature-100 C, and the normal (ambient) air density -1.2 kg/m The forces acting on a hot air balloon include the following: FB buoyancy, FG weight of gas, Fp- weight of payload (including the balloon envelope), and FD drag. Note that the direction of the drag is downward when the balloon is rising Determine the velocity, v, and position, z, of the hot air balloon using the developed MATLAB script. (Round the final answers to three decimal places.) The velocity and position of the hot air balloon are as follows: 3.2 40