I have a question regarding a physics problem that pertains to the conservation

Question

I have a question regarding a physics problem that pertains to the conservation of energy. The problem is from Physics for Scientists and Engineers 6th Edition by Tipler and Mosca. The exact problem is in Chapter 7 and is #15. The actual question reads: Assume that your maximum metabolic rate (the maximum rate at which your body uses its chemical energy) is 1500 W. Assuming a 40 percent efficiency for the conversion of chemical energy into mechanical energy, estimate the following: (a) the shortest time you could run up four flights of stairs if each flight is 3.5 m high, (b) the shortest time you could climb the Empire State Building (102 stories high) using your part (a) result. Comment on the feasibility of you actually achieving your part (b) result. The answer for part (a) is 16 seconds and the answer for part (b) is 6.8 minutes. Please show step-by-step how to get the two answers. I would appreciate a response as soon as possible. Thanks!

Explanation / Answer

      We can assume, the average mass of the person, m = 70 kg       The power P = 1500 W       The efficiency, = 40%       So, the new power is              P' = (40%)(1500 W)                  = 600 W       The height , h = 3.5 m       For four flights, the height h' = 4h                                                      = (4)(3.5 m)                                                      = 14 m                                                      = (4)(3.5 m)                                                      = 14 m _____________________________________________________________ a)       The power related with the work done is                 P' = W'/t                      = mgh'/t       Therefore, the required time is                 t = mgh'/P'                     = (70 kg)(9.8 m/s2)(14 m)/(600 W)                     = 16.00 s ____________________________________________________________ ____________________________________________________________ b)       Here, the height h' = (102)(3.5 m)                                     = 357 m              Therefore, the required time is                 t = mgh'/P'                     = (70 kg)(9.8 m/s2)(14 m)/(600 W)                     = 16.00 s ____________________________________________________________ ____________________________________________________________ b)       Here, the height h' = (102)(3.5 m)                                     = 357 m              Therefore, the required time is                 t = mgh'/P'                     = (70 kg)(9.8 m/s2)(357 m)/(600 W)                     = 408.17 s                     = (408.17 s)(0.1667 min/1 s)                     = 6.8 min                                                               t = mgh'/P'                     = (70 kg)(9.8 m/s2)(357 m)/(600 W)                     = 408.17 s                     = (408.17 s)(0.1667 min/1 s)                     = 6.8 min                   

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