The discussion revolves around determining the original speed of two linked objects in a two-dimensional context, specifically focusing on their momentum before and after separation. The problem involves mass and velocity values for two objects, along with their directional components expressed in terms of angles.
The conversation is ongoing, with participants exploring different methods for vector addition and questioning the necessity of using trigonometry. Some participants express confusion about their diagrams and the correct approach to component analysis, while others provide feedback on the algebraic setup and calculations.
There is mention of potential misunderstandings regarding the initial directions of the objects and the need for clarity on whether they were indeed moving east before separation. Participants also note the importance of maintaining precision in calculations.
tiffanysnsd said:Like I said, I am not very good at trig so my attempt for a diagram got me even more confused (i don't think I am doing it right). This is what I came up with:
http://img199.yfrog.com/img199/8992/vectoraddition.jpg
where
p1' = m1v1'
=(1.9x10^4)(972)
=1.8x10^7
p2' = m2v2'
=(1.7x10^4)(944)
=1.6x10^7
p1' is at an angle of 5.1, p2' is at an angle of 5.9 (which is in the triangle because of the alternate pattern) and 180-5.1-5.9=169.
I know I am wrong, but I hope that by showing my work, you can help me get things right.
Dick said:You don't need a cosine law to add vectors. You just add them. But I may have been misjudging the level of your course. Have you done vectors? If you know the initial direction of both craft is east then you are doing the right thing. You are equating the eastward components of momentum before and after the collision. But I get an answer of more like 954m/s. You might not be keeping enough decimal places. You have the velocities to three decimal places. Try keeping three decimal places. But to two decimal places, your first answer is correct.
Dick said:Did they tell you that both craft were heading exactly east before the separation?
Dick said:But you aren't using vectors in your solution.
tiffanysnsd said:Oh. I guess when you said "Add the two final momentum vectors and equate that to the initial momentum vector and solve for the vector v" that was before you knew they were traveling east?
tiffanysnsd said:If that's the case, how would I approach a graphical trig solution?
Dick said:You would work out the two components of the vectors you labelled p1' and p2', add them and figure out the two components of the vector you labelled p'. Then find it's length.