Optimizing Lifeguard Swim Across a River

[TheronSimon]

Homework Statement

A lifeguard who can swim at 1.2 m/s in still water wants to reach a dock positioned perpendicularly directly across a 550 m wide river.

a. If the current in the river is 0.80 m/s, how long will it take the lifeguard to reach the dock?
b.If instead she had decided to swim in such a way that will allow her to cross the river in a minimum amount of time, where would she land relative to the dock? (10 marks)

Homework Equations

The Attempt at a Solution

I already figured out a with the Pythagorean theorem and so his avg speed is 1.44 m/s and then t= d/V_avg to give me 347,22 sec and so it will take him 345.22 seconds to reach the dock.
but my question is for b. It has me stumped.

 

[tiny-tim]

Welcome to PF!

Hi TheronSimon! Welcome to PF!

b.If instead she had decided to swim in such a way that will allow her to cross the river in a minimum amount of time, where would she land relative to the dock? (10 marks)
…
but my question is for b. It has me stumped.

hint: if x is downriver, and y is across the river,

just concentrate on how fast her y coordinate is increasing

 

[TheronSimon]

but part A. is correct yes?

 

[TheronSimon]

and for part b. if i do
t= 500/1.2
t= 416.66s
so she will take 6.94 min to reach the location and then
d= 0.8*416.66
d= 332.8m
so she will land 332.8 m from the dock in 6.9 min

 

[tiny-tim]

Hi TheronSimon!

and for part b. if i do
t= 500/1.2
t= 416.66s
so she will take 6.94 min to reach the location and then
d= 0.8*416.66
d= 332.8m
so she will land 332.8 m from the dock in 6.9 min

Yes, that's fine (except is it 500/12 or 550/12 ?)

 

[TheronSimon]

550 :P darn typos