$0.860 \textrm{ hp}$

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This is College Physics Answers with Shaun Dychko. This shot putter is pushing a 7.27 kilogram shot put ball to a speed of 14.0 meters per second starting from rest in a time of 1.20 seconds and they are also gonna raise the ball upwards 0.800 meters and the question is what is the power output of this man's arm? So the work done by this non-conservative force due to his arm— it's non-conservative because it's adding mechanical energy to this ball system— is gonna be the change in kinetic energy of the ball plus its change in potential energy. And now its change in kinetic energy is gonna be one-half mass times its final speed squared minus one-half mass times its initial speed squared but with the initial speed being zero, I didn't bother writing that term and then we are gonna add to that <i>mgh</i> which is the change in potential energy as it rises up to height <i>h</i> and then we can factor out the common factor <i>m</i>. Now the power output is gonna be that energy used or the work done in other words, divided by time so it's the rate at which this work is done and so we substitute this expression for the work done and divide it by time. So that's 7.27 kilograms divided by 1.20 seconds multiplied by 14.0 meters per second squared divided by 2 plus 9.80 meters per second squared times 0.800 meters giving us 641 watts and then converting that into horsepower by multiplying by 1 horsepower for every 746 watts that is 0.860 horsepower which is quite impressive for just using 1 arm to be the equivalent power of a horse almost 0.860 times the power of a horse anyway.