Energy added to the elevator (work) = (6,000 N) x (10 meters) = 60,000 joules.
Power = (energy) / (time) = (60,000 joules) / (30 seconds) = 2,000 watts.
Now, here comes the part you've been waiting for: The "horsepower".
We won't go through the history of 'horsepower', where it came from etc.
All you need to know is how it relates to 'watts'.
Here's that answer: 1 horsepower = 746 watts .
So the power of your elevator motor was
(2000 watts) x (1 HP / 746 watts) = 2.681 horsepower (rounded)
Obviously, that unit has nothing to do with real horses, if it ever did.
It's just another name for 746 watts.
Now I WILL tell you how to remember that number ... because it's such a gas.
This story is not true either. But I bet you'll remember it, for a while anyway:
From the detailed entries in Christopher Columbus' log during his
first voyage to the New World, modern scientists have been able to
calculate that when running before a wind of 30 mph, the main sail
of the Nina, the Pinta, or the Santa Maria would have developed
almost exactly 2.0 horsepower.
Columbus discovered America in 1492 .
So each sailing horsepower on that voyage corresponded to
1492 / 2 = 746 watts.
Sorry about that.
The devil makes me do it whenever the subject comes up.