A sailboat moves north for a distance of 15.00 km when blown by a wind from the exact southeast with a force of 2.50 × 10^4 N. The sailboat travels the distance in 1.5 h. How much work was done by the wind? What was the wind’s power? Include all work and a free-body diagram!

***How do I solve this? Thank you!! :)

Question

A sailboat moves north for a distance of 15.00 km when blown by a wind from the exact southeast with a force of 2.50 × 10^4 N. The sailboat travels the distance in 1.5 h. How much work was done by the wind? What was the wind’s power? Include all work and a free-body diagram!

***How do I solve this? Thank you!! :)

jfraser · Answer

work is equal to the magnitude of a force times the distance the force is applied for. The boat is PUSHED by $2.50*10^4N$ for a DISTANCE of $1.5*10^4m$

anonymous · Answer

okay, so i do this?

work done by the wind = (2.50 *10^4) * (1.5 * 10^4) ? @JFraser ?

phi · Answer

I think you use only the "north component" of the wind

anonymous · Answer

so it'd be work done by the wind=(2.50*10^4) * 15.00 ?

phi · Answer

the wind is not blowing directly to the north.  
you want the wind component that is blowing directly to the north.

anonymous · Answer

ohh how can i find that?

phi · Answer

I would draw a picture
|dw:1426874106084:dw|

phi · Answer

does that make any sense?

anonymous · Answer

yes, i think so! and so from here, we have to find what would be the speed blowing in the north direction? :/ is that correct?

phi · Answer

force not speed

anonymous · Answer

ahh okay:) how can we find the force from that image and the information given? :/

phi · Answer

Fnorth = F cos 45

anonymous · Answer

okay!

so work done by wind= (2.50*10^4) * (cos 45) ?

phi · Answer

times the distance in meters
you will get an answer in N-m = joules

anonymous · Answer

ohh like this?

work done by wind = (2.50*10^4) * (cos 45) * (15.00)

phi · Answer

the 15 is in km.  you will want to change that to meters (because we want N-m) not N-km

anonymous · Answer

ohhh okay

so 15.00km = 15,000 m ?

and then work done by wind = (2.50 * 10^4) * (cos 45) * (15,000) 

= 265,165,042.9 joules? <--that's how much work is done by the wind?

phi · Answer

yes, but it makes more sense to write it in sci notation

anonymous · Answer

okay, ermm how would i write that in scientific notation? :/ I'm forgetting the format :(

phi · Answer

same way the force was written
2.65e8 joules
or
$$ 2.65 \times 10^8 \text{ joules} $$

anonymous · Answer

ahh okie yay! :) 

so for the second part, it asks what the wind's power is? how do we find that? :O

phi · Answer

power is energy/time
you will want this in standard units  Joules / sec (i.e. watts)

anonymous · Answer

okay! so energy would be the work right?

so work is what we got above? and the time is given which is 1.5 hrs, which is 5400 seconds? 

so 265,165,042.9/5400= 49,104.63757 joules/sec ? <--power of the wind?

phi · Answer

yes.  kw (kilowatts) looks like the better unit
so
about  49.1 kw

anonymous · Answer

okay, so 49,104.63757  joules/sec converted to kilowatts is 49.1 kw?

:O and so the problem is done then?

anonymous · Answer

oh and what would the free body diagram be again? is that the image that you drew?

phi · Answer

49,104.63757 joules/sec is 49,104.63757 watts
kw is 1000 watts so  49.1 kw
which is about 65.8 horsepower

anonymous · Answer

ahh okay! so the final answer the problem is asking for would be 65.8 horsepower? and thats what is the result of the joules/sec to watts to kilowatts ?

phi · Answer

I would keep the answer in kw
but fyi,  that is about 65.8 horsepower, which you can put in as an aside to show off

anonymous · Answer

haha okay :) 

yay!! so the problem is complete then? :O

phi · Answer

yes

anonymous · Answer

awesome! thank you very much!!!