Collision with orientation, finding velocity

[SuperHero]

Homework Statement

During the warm-up for the 1990 Olympics free skating competition, Debi Thomas, mass 60kg, moving at 5 m/s and looking intently at her coach, collides with Katerina Witt, mass 65 kg,who is smiling at a photographer. The two skaters were moving at right angles to each other.After the collision, they hang on to each other and jointly move at an angle of 37 relative to Debi's original direction. How fast was Katerina traveling before the collision?

The Attempt at a Solution

http://s1302.beta.photobucket.com/user/Rameel17/media/Untitled_zps4d1ae6dc.png.html

This is the diagram that i came up with and here is my calculation:

m1v1 + m2v2 = mtv0
(60kg)(5m/s[E]) + (65kg)(v2) = (125kg)(vo)[E 37 N]

So what i did was i divided the m1v1 and m2v2 seperately with the total something like this:

m2v1 = mtv0
(60kg)(5m/s[E]) = (125kg)(vo)[E 37 N]
300 kgm/s [E]/125kg = (vo)(cos 37[E])
2.4 m/s[E]/ (cos 37[E]) = vo
vo = 3.00512558m/s

so i found the final total velocity, now to find the intial katerine's velocity

m2v2[N] = mtv0[E 37 N]
(65kg)(v2) = (125kg)(3.00512558m/s)(sin 37)
v2 = 3.4779177 m/s

Thats the answer.
is my process correct?

 

[haruspex]

The equations and the thinking behind them are all correct. The verbal explanation could be better. It's more usual to phrase it in terms of components of momentum in the two directions.

 

[SuperHero]

The equations and the thinking behind them are all correct. The verbal explanation could be better. It's more usual to phrase it in terms of components of momentum in the two directions.

Hello, Thank you so much for the reply. What do you mean by conservation of momentum phrases?

 

[haruspex]

In the OP you wrote

So what i did was i divided the m1v1 and m2v2 seperately with the total something like this:

You would not in general be able to separate them so easily, so the reader might suspect you don't understand what you are doing. It would be more convincing to write "by conservation of momentum in the direction of v1..." etc.

 

[Nickie]

I would say that your process is generally correct. However, there are a few things that could be improved upon. Firstly, in your equation m1v1 + m2v2 = mtv0, the v0 should be the final velocity of the combined mass, not the initial velocity. This is because after the collision, the two skaters are moving together at a new, combined velocity. So the equation should be (m1v1 + m2v2) = (m1 + m2)v, where v is the final velocity.

Secondly, in your calculation for finding Katerina's initial velocity, you used the formula mv = m1v1 + m2v2, which is only valid for one-dimensional collisions. Since this is a two-dimensional collision, you should use the formula for conservation of momentum in two dimensions, which is (m1v1 + m2v2) = (m1 + m2)v, where v is the final velocity vector. This means that you have to take into account the direction of the final velocity, which you did correctly by using the sin and cos functions.

Overall, your approach and calculation are correct, but there are some minor errors that could be improved upon. It's always a good idea to double check your equations and make sure they are appropriate for the situation at hand. Additionally, including units in your calculations can help prevent errors and make it easier to keep track of the different quantities involved. Good job on your attempt, and keep up the good work!