A man swims at 1m/s. He is trying to swim across 50m wide river with the length of his body perpendicular to the shore. River current is 2m/s.How long does it take him to cross the river and what's his speed relative to the shore?
I think that his speed is 3m/s and that it takes 50/3 seconds but I'm not sure because he has to swim perpendicular to the shore.
Thank you for any help!
2006-09-28 00:51:30 · 6 answers · asked by 7771313 2 in Science & Mathematics ➔ Physics
well zee, thank you for your help, but it's physics, not math....
2006-09-28 00:59:46 · update #1
___________
~~c ^---->~~~/\
~~~|~~/~~~~50m
~~a|~/b~~~~~~~
~~_|/~~~~~~\/
_____________
Ok so this is a really bad sketch...but this whole problem is about vectors and right triangles.. So basically...a shows his original path with a magnitude of 1 m/s. Path c shows the river current with magnitude 2m/s. Path b shows what his resulting path will be (vector addition of the two velocity vectors). To determine the magnitude of this resulting vector we can use simple geometry. The resulting shape is a right triangle...so let's use the formula c^2=a^2+b^2, where C is the hypotenuse. So...
C^2=1^2+2^2
C=sqrt(1+4)
C=sqrt(5)
So this is his velocity relative to the shore.
The amount of time it takes him to reach the other side is a simple one. Velocity= distance/time...but the distance must be in the same direction as the velocity. Therefore, his time will still be 50m/1m/s = 50s, however he will be pushed downstream and not land across the shore where he intends too.
Good luck...Hope this helps
2006-09-28 01:16:47 · answer #1 · answered by Anonymous · 1⤊ 0⤋
let us say that he starts at point A... if he swims in a direction that is perpendicular to the shore... (that is the direction of his velocity vector, we know this because his body is perpendicular to the shore) then he will take 50 s to cross , but he will end up at a possition that is 100 m down stream...
he will have a speed of 1 m/s in the perpendicular dirrection. But he will also have a speed of 2m/s in his parralell direction.
the parralell velocity does not affect his perpendicular velocity.
you were on the right track... the answer would have been 50/3 if the current and his swim direction were the same....
I hope this answers your question
2006-09-28 01:00:43 · answer #2 · answered by farrell_stu 4 · 0⤊ 0⤋
you have to consider his speed as a vector quantity. just draw two lines with the lengths representing the velocities with their direction. then the hypotenuse of the triangle will give you his speed relative to the shore. as for the time you only have to consider the swimmers speed.
2006-09-28 03:59:42 · answer #3 · answered by Anonymous · 0⤊ 0⤋
I dunno im not so good at physics but if it means the length of his body is PERPENDICULAR (at an angle of 90 deg) then the diagram should be somewhat lyk this....
++++++++++++++++++++++++++++ shore
|
|man
++++++++++++++++++++++++++++ shore
2006-09-28 01:02:09 · answer #4 · answered by Answeraway-YNWA 3 · 0⤊ 0⤋
I THINK THE TIME IT TAKES TO CROOS THE RIVER IS 50/3 AND HIS SPEED IS 3M/S .
2006-09-28 03:05:24 · answer #5 · answered by GENET A 1 · 0⤊ 0⤋
DEPENDS ON WHICH STROKE HE IS SWIMING
2006-09-28 01:09:32 · answer #6 · answered by norman 3 · 0⤊ 0⤋