Another Trig Question

[rarisgod]

A fisherman rows his boat across a river at a constant velocity of 1.2 m/s. There is a current moving down river at 0.24 m/s. If the river is 300 m across, how long does it take the fisherman to row across? How far down the river does the fisherman end up from his point of departure?


I'm a bit too far off with this question, I get that he ends up 59.9 m down the river, but the given answer is apparently 50 m. I haven't looked for the time yet, but thats not difficult after I find the distances.
Please include steps.

[Ziltoid]

Did you listen in class? First you totally forgot cos law and now this.

[rarisgod]

Originally Posted by Ziltoid

Did you listen in class? First you totally forgot cos law and now this.

I didn't ask for discipline.
I havent done problems like this in years. I'm trying to help someone with their math review in a program that is NOT math based and had no high school math prerequisites. I need to be refreshed with this in order to help.

The review in class did not cover incorrect solutions. I didn't forget cos law, it simply wasn't working out to the given solutions so I wanted to know if it was just me or the answers were wrong.

If you don't have anything helpful to say, please don't bother.

[Ziltoid]

Ok, Serious business dude, I was going to help you but I think I'll mind my own business.

[rarisgod]

I just came here for help. People on TB have always been helpful.

[nutdog]

r(t)=d
t=d/r
t=300/1.2=250s
250s(.24m/s)=60m

[rarisgod]

Originally Posted by nutdog

r(t)=d
t=d/r
t=300/1.2=250s
250s(.24m/s)=60m

EXACTLY what I got.
Thanks a lot, the answers must just be flawed.
(whether on purpose or not is another question).

[blendermassacre]

Originally Posted by rarisgod

EXACTLY what I got.
Thanks a lot, the answers must just be flawed.
(whether on purpose or not is another question).

if the answer is in the back of some text book, I'm positive the answer is wrong. My text book has an absurd amount of wrong answers.

[bassybill]

There isn't really enough information in the question to answer this with certainty. Is the 1.2 m/s his diagonal velocity or his velocity at right angles to the current? Read on...

The boat will travel at a slight diagonal, because of the current. This means he will travel further than 300m to cross to the other bank. If the 1.2 m/s velocity quoted is the velocity along this diagonal path, then you need to use vectors (hint - Pythagoras) to calculate the component of that velocity at right angles to the current and then work out the crossing time and the distance travelled downstream (the answers come to 255 seconds and 61m following this procedure).

If the 1.2 m/s is his velocity at right angles to the current, though, the solution given above by nutdog is correct. Either way, the textbook answer seems to be wrong.

[Droot]

Originally Posted by bassybill

There isn't really enough information in the question to answer this with certainty. Is the 1.2 m/s his diagonal velocity or his velocity at right angles to the current? Read on...

The boat will travel at a slight diagonal, because of the current. This means he will travel further than 300m to cross to the other bank. If the 1.2 m/s velocity quoted is the velocity along this diagonal path, then you need to use vectors (hint - Pythagoras) to calculate the component of that velocity at right angles to the current and then work out the crossing time and the distance travelled downstream (the answers come to 255 seconds and 61m following this procedure).

If the 1.2 m/s is his velocity at right angles to the current, though, the solution given above by nutdog is correct. Either way, the textbook answer seems to be wrong.

Without adding any factors to the equation, the answer given is simply wrong. Chalk it up to poor editing.
Droot

[rarisgod]

Originally Posted by bassybill

There isn't really enough information in the question to answer this with certainty. Is the 1.2 m/s his diagonal velocity or his velocity at right angles to the current? Read on...

The boat will travel at a slight diagonal, because of the current. This means he will travel further than 300m to cross to the other bank. If the 1.2 m/s velocity quoted is the velocity along this diagonal path, then you need to use vectors (hint - Pythagoras) to calculate the component of that velocity at right angles to the current and then work out the crossing time and the distance travelled downstream (the answers come to 255 seconds and 61m following this procedure).

If the 1.2 m/s is his velocity at right angles to the current, though, the solution given above by nutdog is correct. Either way, the textbook answer seems to be wrong.

The diagonal is what I originally thought the question was aiming for. The provided answer is 250 seconds but being that the answers are all off, I believe my initial instinct that the time taken must have to do with the diagonal.

I do believe the given solutions are wrong.

Thanks guys!

[funkydjembe]

Okay: (a^2)+(b^2)=c^2

(a^2)+(0.24^2)= 1.2^2

a^2=1.44-0.0576

a^2=1.3824

a=1.1757551 meters per second

300 meters divided by 1.1757551 = 255 seconds

255 times 0.24= 61.2 meters downstream

255 times 1.2=306 meters boat travel

but you should use perfect numbers (square root for ex) to get a perfect answer

[ehque]

Ambigious question.

Usually questions like these should have phrases like "can row 1.2m/s in still water" or "travels at 1.2m/s relative to a point on the shore".

Poor question writing. I say move on. In either case 50 m is wrong.

[funkydjembe]

for every second of boat rowing at 1.2 m/s you are traveling 1.1757551 meters across the 300 meter wide river.

[funkydjembe]

no need for cos in this one as we are dealing a triangle which has 90 degrees (300m across and "x" meters down stream. Pythagoras is enough here

[Febs]

Originally Posted by funkydjembe

Okay: (a^2)+(b^2)=c^2

(a^2)+(0.24^2)= 1.2^2

a^2=1.44-0.0576

a^2=1.3824

a=1.1757551 meters per second

300 meters divided by 1.1757551 = 255 seconds

255 times 0.24= 61.2 meters downstream

255 times 1.2=306 meters boat travel

but you should use perfect numbers (square root for ex) to get a perfect answer

No, this is wrong. Assuming that the river is 300 meters wide at all points and the 1.2 meters per second figure is perpendicular to the current, the downstream current will not impact the amount of time it takes to cross the river. Thus, the only relevant figure for how long it will take to get to the other side is the 1.2 meters per second. It will take 300/1.2 = 250 seconds to reach the other shore.

Since we now know how long it will take the boat to cross the river, we can use the d = r * t formula to calculate that during the time it take for the boat to cross the river, it will travel .24 * 250 = 60 meters downstream during the time it takes to cross the river.

The actual distance the boat travels from the start point is:

a^2 + b^2=c^2
300^2 + 60^2 = c^2
90,000 + 3600 = 93,600 = c^2
c = 305.9411 meters

[bassybill]

Originally Posted by Febs

No, this is wrong. Assuming that the river is 300 meters wide at all points and the 1.2 meters per second figure is perpendicular to the current...

That's the point - it doesn't make that clear in the question.

[funkydjembe]

I would say that it's a given that when you are moving at 1.2m/s and something is pushing you at 0.24m/s in another direction than you have to take that into consideration. It is 1.2 versus 0.24 which is approx. 1.176 meters across the river in the course of 1 second

[nutdog]

Originally Posted by funkydjembe

I would say that it's a given that when you are moving at 1.2m/s and something is pushing you at 0.24m/s in another direction than you have to take that into consideration.

only if you are attempting to compensate for drift, which, given that the problem is to solve for drift distance, one could easily assume you are not trying to do.

Originally Posted by funkydjembe

It is 1.2 versus 0.24 which is approx. 1.176 meters across the river in the course of 1 second

I have no idea how you got this number.

Originally Posted by Febs

the downstream current will not impact the amount of time it takes to cross the river.

^this.

Originally Posted by rarisgod

A fisherman rows his boat across a river at a constant velocity of 1.2 m/s.

This is the given speed he is moving across the river, regardless of his technique.

In addition taking more math classes than I will ever possibly need, I'm a flight instructor. I suspect the basic intent of this problem is to test whether the student understands the concept that "the downstream current will not impact the amount of time it takes to cross the river".

As for the incorrect textbook answers, well, what do you expect from a relativistic society. It is not important to be correct as long as you feel good about your answer.

[bassybill]

Originally Posted by nutdog

only if you are attempting to compensate for drift, which, given that the problem is to solve for drift distance, one could easily assume you are not trying to do.



I have no idea how you got this number.



^this.



This is the given speed he is moving across the river, regardless of his technique.

In addition taking more math classes than I will ever possibly need, I'm a flight instructor. I suspect the basic intent of this problem is to test whether the student understands the concept that "the downstream current will not impact the amount of time it takes to cross the river".

As for the incorrect textbook answers, well, what do you expect from a relativistic society. It is not important to be correct as long as you feel good about your answer.

None of that in any way alters the fact that the question does not specify whether the 1.2 m/s velocity is at right angles to the current or in the diagonal direction actually travelled by the boat.

If the 1.2 m/s figure is taken as the diagonal velocity, then you can consider that as having two components. One of these is the drift due to the current. Resolving the velocity vector for the component perpendicular to the current gives the 1.176 figure.

Either of the solutions in this thread could be correct, but the question is worded in a way that makes it impossible to say which one actually is. The whole point about velocity is that it is speed in a particular direction, and the question does not clearly specify the direction of the 1.2 m/s, regardless of how you read it.