Question

A 3730-kg SUV can climb up a 600-m high hill in one minute (60 seconds). How much is its power output in horse-powers? 245 hp
490 hp
800 hp
373 hp
600 hp

Answer 1

Answer:

490hp

Explanation:

Power is energy per unit of time, an in this case the energy needed is the gravitational potential energy, so we have:

$P=E/t=mgh/t=(3730kg)(9.8m/s)(600m)/60s=365540W$

Since all units are in S.I. we get our result in Watts (Joules/s). To convert to horse power (imperial), we need to know that:

$745.7 W = 1 hp$

Which obviously means:

$\frac{1 hp}{745.7 W} = 1$

So we can write:

$P=365540W=365540W(\frac{1 hp_m}{745.7 W})=490hp$

There is also metric horse power ($735.5 W = 1 hp$), and using this value we get $P=497hp$, although both results are close.