Optimization problem, pretty short, my work included.

[missmathy88]

Please assist me with this problem. Thank you in advanced

A man is in a row boat 4 miles off shore . He needs to get to a point 10 miles down shore.

The man can row 4 MPH and run at a rate of 5 MPH.



At what point along the shore should he land the boat to minimize the time spent getting to the destination??


x^2 + y^2 = z^2

4^2 + y^2 = 10^2

16 + y^2 = 100

y = sqr root of 116 so around 10.75 miles.

is that correct? I was pretty sure derivatives should have been involved though

 

[tkhunny]

I think you have it wrong. To me, I believe your 'y' is the 10 miles, not the water trip.

You don't seem to have used the "5 mph". You'll need hat.

 

[galactus]

Remember, you are minimizing time.

So, find the point on sure he has to land in order to minimize the time spent getting there.

\(\displaystyle t=\frac{d}{r}\)