Physics- Unit: Motion (Question for research), Please help, Thanks.

[arjun90]

Below is a question I was assigned from my mentor for research. Please help me in how to approach the answer (w/o numbers), and write the step-by-step procedure on how to generate the appropriate equation. Thank you for your support.

Homework Statement

A train starts out from New York (suggest you use subscript n) at time T0 moving at Vn miles per hour. Another train starts out from Boston at time T0 moving at Vb miles per hour. The distance from New York to Boston is M miles. Develop an equation that will tell you where the two trains crash into each other (they're on the same track!) measured in miles from New York. Write down your method (reasoning) first, and then implement it. Show all work. Pay attention to signs. (Algebra-type)

Homework Equations

I am a newbie to Physics.

The Attempt at a Solution

My mentor told me that I can't use numbers.

Thank you for your support. Karma.

 

[tyco05]

Firstly you need to choose an origin.
Then you can set up some equations around this.

One train will be moving away from the origin and one will be moving towards it (this is why you need to be careful with your signs).

The distance something moves is given by its velocity mulitiplied by the time it has been traveling. ie. d = vt
e.g. if something moves at 20 mph for one hour it travels a distance of 20 x 1 = 20 miles.

The real trick here is that one train starts at the origin and moves away from it and the other train starts at M and moves towards the origin (it is moving in a negative direction).

You should be able to set up 2 equations; 1 for the distance of each train from the origin.

Then when these distances are equal (set the equations equal) you have your crash.

Note: It wants the distance from New York, so make that your origin.

 

[arjun90]

From what the question is stating both trains are starting from their origins and the point where they crash has the same proximity from their origin. My teacher told me that my resulting equation should be stated as x=something (only one equation, however; you are showing me two). Can you please see if you can combine the two and make the equation as one reason?

I should really be asking how should I write out the distance from the origin in equation terms? (from you explained to me in your very last point). That would be very helpful. Thank you very much. I really do appreciate it.

Firstly you need to choose an origin.
Then you can set up some equations around this.

One train will be moving away from the origin and one will be moving towards it (this is why you need to be careful with your signs).

The distance something moves is given by its velocity mulitiplied by the time it has been traveling. ie. d = vt
e.g. if something moves at 20 mph for one hour it travels a distance of 20 x 1 = 20 miles.

The real trick here is that one train starts at the origin and moves away from it and the other train starts at M and moves towards the origin (it is moving in a negative direction).

You should be able to set up 2 equations; 1 for the distance of each train from the origin.

Then when these distances are equal (set the equations equal) you have your crash.

Note: It wants the distance from New York, so make that your origin.

 

[saket]

How about this approach?
Since they are going to crash, they together are going to cover the total distance between New York and Boston, M.
Further, since they are moving towards each other, their relative speed will sum up. That is to say, New York train would approach Boston train with a speed Vn + Vb.
[Satisfy yourself from common life experience, if you are unfamiliar with relative velocity. If the New York train alone had moved (with Boston train standing at Boston itself), it would have taken more time to crash, than when Boston train is also approaching it, ain't it?]
So, total distance = M, speed of approach = (Vn + Vb)
Calculate time t for the crash.
And then calculate how much the New York train will move in this time. Using, distance = speed * time. (Note that speed of New York train is Vn.)
Thereby, setting up your co-ordinate system you can identify the coordnates, right?

 

[andrevdh]

I think you should rather gives us your thoughts on the problem and then we can discuss it with you here. How would you attempt it?

 

[arjun90]

We are measuring constant velocity here. It does not vary, thus; I don't know how we will be able to use d=vt

Firstly you need to choose an origin.
Then you can set up some equations around this.

One train will be moving away from the origin and one will be moving towards it (this is why you need to be careful with your signs).

The distance something moves is given by its velocity mulitiplied by the time it has been traveling. ie. d = vt
e.g. if something moves at 20 mph for one hour it travels a distance of 20 x 1 = 20 miles.

The real trick here is that one train starts at the origin and moves away from it and the other train starts at M and moves towards the origin (it is moving in a negative direction).

You should be able to set up 2 equations; 1 for the distance of each train from the origin.

Then when these distances are equal (set the equations equal) you have your crash.

Note: It wants the distance from New York, so make that your origin.

 

[HallsofIvy]

From what the question is stating both trains are starting from their origins and the point where they crash has the same proximity from their origin.

Tyco05 said "choose an origin"- i.e. choose a coordinate system. That is not necessarily the same as the "origins" of the two trains. He further said "It wants the distance from New York, so make that your origin." That is, since the question specifically asks you to find the distance from New York to the point where the two trains meet, it is simplest to use New York as the origin of your "coordinate system".

Draw a picture. Your "coordinate system" will be a straight line from "New York" to "Boston". New York will be at "0". What number corresponds to Boston? Write an equation for the position of the train leaving New York: in other words, at any time t, what is its distance from New York? Write an equation for the position of the train leaving Boston: in other words at any time t, what is its distance from New York (not Boston). The two trains will crash when they have the same distance from New York. Set those two equal and solve for t. Once you have found that, you can put t back into either of those two position equations and solve for the distance from New York.