A factory requires an engine to lift 2000 kg of metal through a distance of 12 m in 1 minute. Determine the minimum horsepower of the engine needed for this task.

Step-by-step solution

Work done by the engine to lift the metal is given by: W = mgh Substituting the given values ( m = 2000 kg , h = 12 m , g = 9.8 m/s ^2 ): W = 2000 9.8 12 = 235200 J The time taken is t = 1 min = 60 s . Power P is the rate of work done: P = W t = 235200 60 = 3920 W Converting the power into horsepower ( 1 hp = 746 W ): P = 3920 746 5.25 hp Using g = 10 m/s ^2 , we get P = 2000 10 12 60 = 4000 W , which gives P = 4000 746 5.36 hp . The closest value among the given options is 5.3 hp .