Will medal and fan for your consideration. A swimmer swims 75 meters across a river at 1.5 m/s. The river is flowing at 4m/s. How long does it take to swim across the river? How far does a person with a towel need to wait downstream to meet the swimmer as he climbs up the opposite bank? If a pedestrian walks across the bridge spanning the same river at 1.5m/s, how long will it take said pedestrian to cross?

Question

jmartinez638 · Answer

@matt101 I hope you aren't mad I am calling on you so much :s

matt101 · Answer

It's no trouble that's why I'm on here!

How would you go about solving this question?

jmartinez638 · Answer

I know that the way the direction that the swimmer would end up going, that is, diagonally with the current from where he started, would look kind of like a piecewise function if you were to graph it.

jmartinez638 · Answer

So you can calculate the distance he has to go, which would end up being just slightly over 75 meters if the current were less than 4m/s, but unfortunately it is so. Knowing that that distance is longer than 75 meters straight across, and he is going at a set velocity of 1.5m/s, he would take longer than the pedestrian.

jmartinez638 · Answer

so all we have to do is calculate how long he ends up having to swim using vectors, then using the same vectors we can see where he will end up, and a pedestrian walking 75 m at 1.5m/s is the easy part so.

jmartinez638 · Answer

@matt101 ^^ this look right?

matt101 · Answer

Sort of. To find the time it takes to cross the river, you only need to consider stuff happening in the direction perpendicular to the bank. The person is swimming in this direction, so his speed will be a factor. The speed of the river is not operating in this direction (it's parallel to the bank), so you don't need to worry about vectors for this part of the question at least.

It's the next part, where you're asked about how far downstream a friend would need to wait, that requires you to consider both directions of movement.

jmartinez638 · Answer

So basically, the movement of the river does not affect how long it will take him to cross?

jmartinez638 · Answer

I guess I'm having a little trouble then :d

matt101 · Answer

That's right!

Pretend you're on a boat. You can walk from one end to the other no problem, even if the water around you is moving the boat somewhere. The water isn't changing your ability to walk from one end of the boat to the other, whether the water is moving at 2 m/s or 20 m/s.

So in this case, the person is swimming at 1.5 m/s for 75 m across the river. How long does that take?

Note that 75 m isn't the ACTUAL distance he travels - it's just the perpendicular (to the river bank) component of the displacement vector. The actual distance traveled is much more, diagonally downstream as you've said. However, the speed of the water adds to the person's velocity, causing his GROUND speed to be faster. But, the faster actual speed makes up for the longer actual distance, so that the time of the trip is still the same no matter what speed the river is flowing at!

jmartinez638 · Answer

50 seconds for him to cross the river

matt101 · Answer

Right! So his trip is 50 s long. Now we want to figure out how far downstream he traveled in that time. His DOWNSTREAM speed is coming only from the river, which is moving at 4 m/s. The speed he's swimming at doesn't contribute to his downstream movement, because it's perpendicular to it.

So 4 m/s for 50 s - what downstream distance is that?

jmartinez638 · Answer

200 meters

matt101 · Answer

Right. Now the last question. What's the answer?