Related Rates The sailor sails his boat at a constant speed of 12km/h staying 4km from and parallel to a straignt shoreline. How fast is the boat approaching a lighthouse on shore where boat 5km from the lighthouse?

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Related Rates The sailor sails his boat at a constant speed of 12km/h staying 4km from and parallel to a straignt shoreline. How fast is the boat approaching a lighthouse on shore where boat 5km from the lighthouse?

Mathematics
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|dw:1433040585514:dw| I'm not sure though...
|dw:1433040673042:dw|

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Other answers:

oh, okay
I think just take distance/ velocity = time
The 12km/h, is going negative?
how?
12km/h = 12km/ 60 minutes, that is 1minute/ 0.2 km you have 5 km, then, it takes 25 minutes to finish the distance, right?
I remember something about -12km/h from my teacher, but I'm not sure though.
if velocity has negative sign, that shows the replacement is opposite way to what you define positive direction. In this case, they use "speed" not velocity, hence, no negative here, period.
hey still stuck on this
Yes @rational I'll be right back, I have to eat dinner
I'm back @rational
so want to know the rate of change of the 'hypotenuse' of this triangle; what can we use to model the length of the hypotenuse?
|dw:1433045913122:dw|
d^2 = b^2 + 4^2 implicit derivative gives us 2d d' = 2b b' d' = b' b/d we know b' and b, and can determine d
or we know b' and d ... and can determine b either way
b=3?
|dw:1433046508888:dw| ???
Given dx/dt =12km/h, find dz/dt=? when z=5km x^2+y^2=z^2 (2x)(dx/dt)+(2y)(dy/dt)=(2z)(dz/dt) ???
May the answer be 36/5=dz/dt??
36/5 looks good!
My teacher said something about -12km/h, but dont know why...
Should it be -36/5km/h?? hmmm... :/
yes, because the distance between lighthouse and boat is reducing
What do you mean?
in the diagram the boat is approaching near to the light house, yes ?
yes
since the distance is decreasing, the velocity is negative
the distance is decreasing at a rate of 36/5 km per hour is same as saying the distance is increasing at a rate of \(\color{red}{-}\)36/5 km per hour
i have a debt of $100 is same as saying i have -$100
Oh I see! Thanks lots!

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