Question

A swimmer is caught in a riptide 300 m directly off the Jersey Coast. The current is flowing at 1 m/s, 30 degrees from the shoreline and to where the swimmer is located. The swimmer determines that he has the strength to swim for 20 minutes and thus, must follow the shortest path. How should he direct himself with respect to the shoreline and how fast does he need to swim? Blue: 300 m Red: Current Hegre Yellow: Shoreline Star: Swimmer 30 V es Draw the swimmer's heading and speed relative to the water on the above diagram. If the rip current suddenly disappears as the swimmer swims at his decided rate and heading, how far does he end up swimming and how much time will this take?

Answer 1

The problem can be describes as follows:

wher ur is velocity of the river. Let us assume that man is swiming with a speed of um and will start at an angle with horizontal as shown below: So the veocity of man and river can be shown as:

Th man can swim for 20 min and he has to travel in the shortest path. Now the sortest path from the mans location to shore is a straight line. Hence he will be trying to travel in that path.

Now we will consider the two compnents of the velocities:

Vertical:

where uv is the relative velocity of man in the direction of shore. or that is the velocity whith which the man will be swimming towards the shore:

Horizontal:

this should be equal to 0 as the man wants to travel in a straight line perpendicular to the direction of uh. Another way of looking at this is, if uh is a psitive value, there will be a displacement in horizontal diection and it deviates the man from straight line.

equating uh=0,

and using distance = speed x time,

substituting in eq (1) and converting minutes to seconds,

eq (3) / eq(2)

substituting angle in (3) gives,

Now if the current suddenly disappears, the velocity of man looks like the folowing diagram:

The veoclity may be resoved into vertical (uv) and horizontal (uh) components.

Now the time taken to reach the shore will be different. Lets find that using,

Now distance travelled in horizontal direction can be calculated as:

Hope this helps.

Happy learning