Question

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.
If the current in the river is 0.80 m/s, how long will it take the lifeguard to reach the dock?
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?

Answer 1

Her resultant speed is perpendicular to the flow of the river.
Thus resultant velocity, using Pythagoras theorem,
V=√(1.2²-0.8²)
=√(0.8)
=0.8944 m/s

Time to cross river
=550m/0.8944 m/s
=614.9 s
=10 minutes 15 seconds, approx.

to cross as rapidly a possible, the crossing speed is exactly 1.2 m/s,
time = 550/1.2
= 458.3 s
= 7min. 38.3 sec.