A bear swims across a river 100M wide @ 5m/s due east. The river flows due South at 10m/s.
How long does it take him to cross the viver?
What is his displacement from the starting point?
What is his speed form the point of view of a person standing on the shore?
before I start, is this the same as what we did in class along with an additional question?
ReplyDelete-Will F
Yes, the visible speed from the person on the shore should be 10 m/s because it would be difficult to see him going east, if you are facing west
DeleteUnless, it is a very clear day and you can see the bear gradually getting larger as it approaches. But even in that situation, it would be hard to gauge how fast it is traveling and you would probably just assume that it is traveling South because the velocity that the river generates is double that of the bear swimming.
Deleteyou want to do the easiest possible situation because they are millions of what ifs.
Deletethe clear day would be the easiest situation but even in that case it would be hard to discern the speed of the approach so your brain would process the southern speed instead
DeleteAre we supposed to put the answers up? Or is this blog just supposed to be used for questions?
ReplyDelete-Kevin Meglathery
I don't think you should put the answers up because then other people will just copy them. You should probably just do them in your notebook and discuss in class
DeleteOr maybe once more people see the assignment and start to post on this thread, you can post the answers in order to compare with other people
DeleteI agree with Noah. The blog post was put up in order to start a discussion on how to come to a final solution. Once a majority of us are on the same page, we can probably start putting up what we got for answers.
DeleteMr. Crane said the blog can be used for answers after most questions are answered and you should explain your answer.
Delete-Skylar Young
Why does it matter that the river is flowing south at 10m/s if the bear is traveling east? That should only affect the displacement, not the time that it takes to cross the river.
ReplyDeleteExactly.
Delete-Kevin Meglathery
It matters because it does effect the displacement
DeleteIt affects the time because if the bear was traveling north, it would be going against the force of the water, which would cause it to take a longer time to get to the other side. I don't think it would affect the displacement, though, since it would still travel the same distance as it did south, even if it went north. It would just take a longer time.
DeleteIf the bear was going north, he would actually be moving backwards because the river moves faster than he does. In this case, his displacement would increase infinitely until he finally realized that he was getting farther away from the picnic basket.
Delete-Kevin Meglathery
The rivers speed does not effect the time it takes the bear to cross the river. But the speed of the river does effect the displacement.
DeleteBut the bear is not going north so we can disregard the southern speed for everything except the displacement
DeleteKara, I disagree I believe the river speed affects the bear's time because it is pushing him on a greater slant which will effect his time as well as his displacement.
DeleteWe have to use the Pythagorean theorem to find the displacement right? We know that one side is 100M, the width of the river, and the other side which will be the distance that the south river stream will take the bear if only looked at for the time that it takes it to cross the river. Then for the hypotenuse, we square both values, add them, and take the square root of it right?
ReplyDeleteYes, since it makes a right triangle.
DeleteI just got to this part. I dont understand what the distance the bear will travel.
DeleteSO on one leg of the triangle is 100M then on the other one it is time it takes for bear to cross?
DeleteMimi you are correct the one leg is 100 m, but the other leg would be the distance the bear traveled vertically. and then you would use Pythagorean theorem to find the hypotenuse
Deletewell we dont know the distance travelled vertically. I dont understnad this
DeleteYou need to calculate the distance traveled vertically by multiplying the time it takes the bear to get across by the speed of the river.
DeleteOne side is 100 meters because that is the width of the river, the other side is the time it takes the bear to cross the river multiplied by 10 meters per second. You square both values, add them together, then take the square root of that sum and that will be the bear's displacement
DeleteYes it will make finding it a lot easier. You will be able to find the third leg, or the displacement.
Delete100^2+200^2=50000
Deletesquare root of 50000 is 223.6067977 which I believe is 224 using sigfigs
So would it be, 100^2 + 20^2 = 10400 sqrt 10400 = 102? What do I do with 10 m/s?
DeleteWhere did you get 200?
DeleteDerek, when Mr. Crane made the graph on the board he told us the bear went 100 meters horizontally and (200) meters vertically, which is where the 200 comes from.
DeleteDo we do this problem as well as the squirell problem from left to right?
ReplyDeleteWe finished the squirell problem in my class, but if you didn't in yours, you could definitely complete it now so you can discuss it in class next time.
DeleteYea Molly
DeleteOk! thats what I thought. I was just making sure it was for our class too
DeleteFor comparison purposes (not honor code violations) what did you get as the status of the squirrel after the car passed? Alive or deceased?
DeleteI found that the squirrel is still in existence. The squirrel would take 3 seconds to cross the road. The car would take 1.2 seconds to travel the 30 meters that we are looking at. You might think that the car would be able to cross all 30 meters while the squirrel is still on the left side of the road, I examined this and found that the squirrel would be in the safe zone while the car is passing all 30 meters because the 7.5 meters of safe zone divided by the 1.2 seconds that it would take the car to travel the 30 meters is 6.25 meters, which is less than the 7.5 meters, so the squirrel is safe. However, it did not survive the way we thought it would. Instead of being quick enough to cross the street faster than the car, it was slow enough that the car would speed past the squirrel before it even has a chance to step into the right lane of the road that the car is on
DeleteI set it up exactly like the squirrel problem.
DeleteI am confused on how to get: What is his speed form the point of view of a person standing on the shore? can anyone help!?
ReplyDeleteWell for his general speed, I created another right triangle. It travels south 10 m/s and east 5 m/s, so that's your two "lengths" for the triangle. Then you use the Pythagorean Theorem to find its speed traveling diagonally.
DeleteWhat I'm not sure about, though, is why it matters what the point of view of the person is. Wouldn't it still be swimming at the same speed whether the person is on the shore or not?
DeleteThe speed from the view of a person from shore simply means the speed you see the bear moving.
DeleteThe bear moves both 5 m/s horizontally and 10 m/s vertically SIMULTANEOUSLY, thus the bear is moving diagonally.
You use the horizontal speed of the bear (5 m/s) and the vertical speed (10 m/s) as sides of a right triangle to find the hypotenuse, which is the speed you see the bear moving from the shore.
-Billy Potts
Thanks, I think I get it now
DeleteAren't velocity and speed different things? If it is moving 5 m/s than thats velocity and speed would be 10mph right? Im confused about this part.
DeleteI disagree with Billy. The bear is moving diagonally, however, it would be hard for a person standing 100 meters away to see that the bear is coming toward him. You would look at the bear and quickly process that it is floating downstream with the river at 10 meters per second because that speed is significantly faster and easier to notice because it is moving from side to side as opposed to up and back. It would take a long time for the human to notice that the bear is slowly getting larger as it is approaching.
DeleteMimi, you are right. It was most likely just a typo, but it is enough information to grasp the concept.
DeleteThat clears up a lot for the point of view part of the last question. Thank you NO HA!
DeleteYou are very welcome
Deletethanks Noah!
DeleteI dont get it. The bear is heading east but the river is heading South. Is the speed of th river irrevlevant?
ReplyDeleteIt is going diagonal. Look in the posts above to get the explanation.
DeleteThe speed of the river is relevant, if you are in a river with still waters, it is going to be different then if you are in a river with 50 mph current.
DeleteMr. Crane explained to my class that the speed of the river is relevant. He said it is like going on a down escalator and walking from the left side of the step to the right side of the same step. You are moving from left to right as you move down the escalator. The movement of the escalator does not effect your movement of left to right, but you are still moving down the escalator. The bear is swimming across the river, and the river is taking the bear down stream. The rivers speed doesnt effect the bears speed but it would create a diagonal.
DeleteThe speed of the river is relevant to the total displacement and the speed of the bear relative to the person on the shore. It is irrelevant to the time it takes him to cross the river.
DeleteJust ignore the velocity of the river for everything except for the displacement. There, you will have to use the pythagorean theorem as seen in an above post.
DeleteThe speed, direction and time are all relevant in this situation. Make sure you stick with the simplest possible scenario for what you're trying to solve.
DeleteThe speed of the water will affect the displacement. Without it, the displacement would be far less and easier to find.
DeleteJames, you are right. The velocity of the river increases the displacement just like measuring one side of a television would not be as much as measuring the diagonal
DeleteWhat is the speed of the bear from someones view standing on the shore? Would that be the hypotenuse? If it is the hypotenuse, what would be the other two sides?
ReplyDeleteYes the speed of the bear from someones view standing on shore would be the hypotenuse. The other 2 sides would be 10 m/s and 5 m/s because 10 m/s is the speed of the river and 5 m/s is the speed the bear is swimming.
DeleteKara is right. The sides that create the right angle of the triangle are the speeds 10 m/s and 5 m/s. 10 m/s south (downstream) and 5 m/s east (across the river).
DeleteOkay thank you
DeleteTo get the time, how do i set up the right triangle?
ReplyDeleteTo set up the triangle you draw a diagonal line from where the bear started to where the bear ended. You then use the Pythagorean Theorem to solve for this distance.
Delete-Skylar Young
Don't use pythagorean theorem for the first problem! If you think about it, the southern velocity of the river will not affect the time! It will only change the displacement. That velocity is downward and would only affect the bear's velocity if it was going upward! Since the bear's velocity is side to side, it shouldn't affect the time that it takes to cross the river.
DeleteIf you set up a right triangle and use the pythagorean theorem, it's a lot easier. Use the 5 m/s from the bear and the 10 m/s of the river to set up the triangle. The 5 m/s is horizontal, while the 10 m/s is vertical. Connect them to form a right triangle.
ReplyDeleteNo, you have to multiply the 10m/s of the river flowing south by the time that it takes the bear to cross the river. Therefore, you must solve the problems in the order that they are displayed.
DeleteMr. Crane said using the pythagorean theorem was fine and is much easier to use.
Delete-Skylar Young
Yes, I was just saying that you need to use the information obtained from the first problem and use it as values for pythagorean theorem in the second and third problems
DeleteIsn't this what we did in class on friday?
ReplyDelete-Matt Nazha
Essentially, yes. Some classes might not have gotten as far as we did.
Delete-Kevin Meglathery
My belief is yes, but I am not completely sure.
DeleteIf you were in period 3 then yes it is the exact same thing. Other classes did not get to this assignment.
Delete-Skylar Young
The time is not changed by the rivers speed right?
ReplyDelete-Skylar Young
No skylar, just the displacement
DeleteMatt, only some classes were able to complete this in class. Mod 7 didn't even finish the squirrel problem when it was moving from the left side of the road to the right
ReplyDeleteFor anyone confused, setting #2 and #3 up as a right triangle and using the Pythagorean theorem to solve really really helps!
ReplyDelete-Katie Morgenstern
Is this the same as what we did in class? I am a little confued.
ReplyDeleteIf you are referring to the squirrel problem, it would be the same thing only with another aspect, displacement, added
DeleteMr Crane, do you think enough people have seen this thread and done the work that it is safe enough to post the answers for comparison purposes or should we save that for class?
ReplyDeleteI say we just compare them. That what he said this blog is for.
DeleteIn AP physics we usually talk more about our process than the answer. So, I think he'd rather you discuss how you got to the answer (pythagorean theorem, etc) and why rather than just your number answer, if anything.
DeleteWell, if you explain how you got your answer, then we are able to determine where someone may have made a mistake finding their answer.
DeleteThat is true. Shall we compare processes then? I used multiplication disregarding the southern velocity for the first one. The displacement was pythagorean theorem. And for the speed from the person on the shore, I at first used logic and reasoning but now I can see that I may or may not have been wrong because other students used pythagorean theorem for this problem as well
DeleteDerek, I also set it up like the squirrel problem and I'm pretty sure I did not get the right answer.
ReplyDeleteI just set up the picture the same way as the squirrel problem. I made a
DeleteRiver just like the street in the squirrel problem and drew a bear going across the river. I also drew a right triangle to help me find the answers to a couple questions.
Ok thanks. But the variables aren't the same right?
DeleteNo because they are different questions.
DeleteWhat do you mean by the variables?
DeleteIn class today the best way I found out to solve this was using a graph and chart.
ReplyDeleteI preferred a picture/chart/graph hybrid. It was a square river that had labels for meters and and time along each side. Then I plotted dots and found that they were going downwards diagonally onto the right side. This was visual evidence that the southern 10 m/s velocity of the river did not affect the time that it takes the bear to travel all 100 meters, only the displacement
DeleteWould it be a different formula if we said the bear was forcing itself upstream? Against the current?
ReplyDelete-Catherine Samara
I believe all that you would do differently would be to use a little bit of vector math. Since it would be going north 5m/s, and the river is flowing south 10 m/s, the bear would travel south at 5 m/s because 10m/s (south) - 5m/s (north)= 5m/s south
DeleteVector math may be a little confusing. But if the bear is supposedly forcing itself upstream that would be kind of pointless because it would take longer and be more tiring.
DeleteThe formula would actually be easier because everything is in the same direction. Like Noah said, it would become simple subtraction.
Delete-Kevin Meglathery
Thanks kevin. All you have to do is see which velocity is stronger. The bear can't move upstream because the downstream velocity is greater
DeleteI thought the best way to solve was using the Pythagorean theorem. That is what Molly and I used in class and we thought it was useful since it was making and triangle and only having to solve for the hypotenuse.
ReplyDelete^agreed
DeleteI'm still a little confused. From the point of view of a person he seems to be going a different speed but how would you find out what it is? wouldn't it look like he is going slow? can anyone help because i'm also not sure on if there is another formula we are supposed to be using.
ReplyDelete~Gianna B.
I think that this question is a lot simpler than people think it is. A person on the shore would only be able to notice one speed. They wouldn't see the bear going horizontally and vertically. They could only see one velocity. That velocity is the hypontenuse on a right triangle with bases 5 and 10.
Delete-Kevin Meglathery
try using the pythagorean theorem with 5 m/s on one side and 10 m/s on the other side. find the hypotenuse (the speed someone on shore will see the bear)
Deletewhat variables could effect the bear crossing the river?
ReplyDeleteThe bear losing energy and slowing down
DeleteObstacles in the river like rocks
Rival bears looking for a fight
Change in speed of the river (would only affect displacement)
Changing direction of current
Depth of river (possibly allowing him to walk across)
I'm sure there are others, but that's all I've got right now.
-kevin Meglathery
Ari there are many possible variables that could effect the bear, but as Mr. Crane said in class we are looking for the easiest possible solution without having to worry about unnecessary stuff to figure out as well
DeleteDoes anyone know if this is due tomarrow?
ReplyDeleteSeam our class already did this problem in class so we worn't be going over it. This question is for the other classes.
Delete-Skylar Young
Ok. how do we find the distance between the first and second bear?
DeleteI used the Pythagorean Theorum. This tiem is one side of the triangle and the distance in the river is the other side of the triangle.
Delete-Skylar Young
Skylar, i understand that part, however doesnt the speed of the river, affect the landing spot of the bear, since the bear is going only 5 m/s, and the river is going 10m/s. wouldn't this casue the bear to take longer than normal, because in class, they said it cancelled out or something similar to that, and i beleive the bear would end up farther down the river?
DeleteThe bear does end up farther down the river. 200 meters farther down. But this does not effect the time it takes the bear to cross the river. It still takes the bear 20 seconds. These two numbers creat the two legs of the triangle.
Delete-Skylar Young
Mr. Crane hasn't posted the blog for the "Shoot for an 'A'", right?
ReplyDeleteHe just posted it!
Delete