Ascending hot-air balloon—M . A spherical hot-air balloon of diameter 40 ft and deflated mass 500 lbm is released from rest in still air at 50 ◦F. The gas inside the balloon is effectively air at 200...

Ascending hot-air balloon—M . A spherical hot-air balloon of diameter 40 ft and deflated mass 500 lbm is released from rest in still air at 50 ◦F. The gas inside the balloon is effectively air at 200 ◦F. Assuming a constant drag coefficient of CD = 0.60, estimate: (a) The steady upward terminal velocity of the balloon. (b) The time in seconds it takes to attain 99% of this velocity. The density of air (lbm/ft3) is 0.0774 at 50 ◦F and 0.0598 at 200 ◦F. The table of integrals in Appendix A should be helpful.