- #1
recon
- 401
- 1
Joe is swimming in a river 50 metres away from the bank. He would like to get back to his parents who are 100m along the river bank from where he is. If he can swim at 3 m/sec and run at 7m/sec, how far along the bank should he land in order to get back as quickly as possible?
So far, I've figured out how to do this:
Let [tex]x[/tex] be the distance along the bank that he should land in order to get back as quickly as possible.
Since he's 50 m away from the bank, he has to swim a distance of [tex]\sqrt{x^2 + 50^2}[/tex] metres, and then run a distance of [tex]100-x[/tex] metres.
The total amount of time taken to do this is [tex]\frac{7}{100-x} + \frac{3}{\sqrt{x^2 + 50^2}}[/tex].
Now, I can tabulate everything on an Excel spreadsheet, and figure out the answer from there, which is: he should land roughly 23.7 metres along the bank from where he is. Is there a more elegant way of getting around this?
So far, I've figured out how to do this:
Let [tex]x[/tex] be the distance along the bank that he should land in order to get back as quickly as possible.
Since he's 50 m away from the bank, he has to swim a distance of [tex]\sqrt{x^2 + 50^2}[/tex] metres, and then run a distance of [tex]100-x[/tex] metres.
The total amount of time taken to do this is [tex]\frac{7}{100-x} + \frac{3}{\sqrt{x^2 + 50^2}}[/tex].
Now, I can tabulate everything on an Excel spreadsheet, and figure out the answer from there, which is: he should land roughly 23.7 metres along the bank from where he is. Is there a more elegant way of getting around this?