Vector Parameters: A and B are two campsites whose coordinates are measured in km....

[MW21]

Hello,

Would someone be able to help me with this problem (it's starting to annoy me)
Campsite Problem:

A and B are two campsites whose coordinates are measured in kilometres. A hiker leaves A on a path defined by:

x[t] = 3t + 3 x(t) .
y[t] = 4t + 2
time is in hours

At the same time, another hiker leaves B along a path defined by:
x[t] = 4t - 1
y[t] = 3t + 6

a) what are the coordinates of the campsites?
b) what are the walking speeds of each hiker?
c) what is the distance between the walkers at any time?


Thanks in advance,

 

[Deleted member 4993]

Hello,

Would someone be able to help me with this problem (it's starting to annoy me)
Campsite Problem:

A and B are two campsites whose coordinates are measured in kilometres. A hiker leaves A on a path defined by:

x(t) = 3t + 3 x(t) is not a function, it's a subscript.
y(t) = 4t + 2

At the same time, another hiker leaves B along a path defined by:
x(t) = 4t - 1
y(t) = 3t + 6

a) what are the coordinates of the campsites?
b) what are the walking speeds of each hiker?
c) what is the distance between the walkers at any time?

This question seems reasonably easy to solve, but solving using vectors is where I am having trouble.

Thanks in advance,

Please share with us the work you have done without using vectors.

 

[Steven G]

Hello,

Would someone be able to help me with this problem (it's starting to annoy me)
Campsite Problem:

A and B are two campsites whose coordinates are measured in kilometres. A hiker leaves A on a path defined by:

x(t) = 3t + 3 x(t) is not a function, it's a subscript.
y(t) = 4t + 2

At the same time, another hiker leaves B along a path defined by:
x(t) = 4t - 1
y(t) = 3t + 6

a) what are the coordinates of the campsites?
b) what are the walking speeds of each hiker?
c) what is the distance between the walkers at any time?

This question seems reasonably easy to solve, but solving using vectors is where I am having trouble.

Thanks in advance,

I'll try to give a hint. 1st of all why do you say that x_t = 3t + 3 is not a function of t? In order to know what x equals you need to know what 3t + 3 equals. And to know what 3t + 3 equals you need to know what t equals. Hence, x is a function of t.
Now what information does x(t) = 3t + 3 and y(t) = 4t + 2 give you for values of t? What do you think t means? What do you think the units of t are? What about the units of x and y. Until you can answer these questions you really will not understand the problem

 

[Dr.Peterson]

A and B are two campsites whose coordinates are measured in kilometres. A hiker leaves A on a path defined by:

x(t) = 3t + 3 x(t) is not a function, it's a subscript.
y(t) = 4t + 2

At the same time, another hiker leaves B along a path defined by:
x(t) = 4t - 1
y(t) = 3t + 6

a) what are the coordinates of the campsites?
b) what are the walking speeds of each hiker?
c) what is the distance between the walkers at any time?

This question seems reasonably easy to solve, but solving using vectors is where I am having trouble.

First, I think all you are saying about "not a function" is that you don't intend x(t) to look like function notation, but like a subscript. Regardless of the notation, it is clear that x is a function of t.

The difficulty I have with the problem is that you haven't quoted a definition of t. In order to answer part (a), we need some idea of that. We can assume that t is the time, perhaps in hours, since each left his campsite, but we don't know that unless we are told. Are we? It is entirely possible that t is just an arbitrary parameter, except that then we would be lacking far too much information.

If so, then we can easily find the coordinates of the campsites, especially for part (a).

I don't see that vectors are particularly helpful there; are you saying that you are required to use them for all three parts? For part (b), you might just directly read off the vector velocity; or if you are learning calculus, you can find it as a vector derivative. Then you'll need to find the magnitude, since they asked for speed, not velocity. The answer to part (c) will be a function of t.

Perhaps you can see how important it is for us to know the context of your problem (and the entire problem), in order to judge how (and whether) vectors should be used. And, as has been mentioned, telling us how you solved it without vectors would give us a very good starting point for helping.

 

[MW21]

My apologies,
I left out the section of the question where it states that time is in hours.

I managed to figure out the question, I was just slightly confused as I have never encountered parametric equations before, and was overcomplicating the question, in terms of attempting to use the components of the course that I already knew.

as for the conundrum where I said that t was not a function, I was simply referring to the notation and knew that x and y were functions of t, and was just being careful as I didn't really know what I was dealing, with and wanted to be sure, just in case the notation changes the meaning of the question. (i need to be careful with my communication).

a) was easy as the location of the campsite was determined by substituting time equals zero into the equation, therefore, the locations of the campsites are (3,2) and (-1, 6)

b) by taking the distance travelled in one hour (determined from velocity vector, via Pythagoras) the speed was determined (5km/hr)

c) the distance at any time was determined by finding the x component of both equations (-(t-4)) and the y component (t-4), which when equated (using Pythag), results in the distance at any time being equal to the square root of 2 multiplied by t-4.

I'm sorry for any confusion that I caused to anyone, and for wasting your time. I was just really confused as my teacher just sprung this on us without explaining anything (i thought it was a new topic)

would anyone happen to know any examples similar to this one/know where i can find some? I would like to practice these sorts of questions to gain a better understanding.

thanks for your time, and again sorry for my incompetence.