Okay, so... Here I am, having another algebra problem... This is the problem:(adsbygoogle = window.adsbygoogle || []).push({});

A glider of mass 0.141 kg is moving to the right on a frictionless, horizontal air track with a speed of 0.740 m/s. It has a head-on collision with a glider 0.310 kg that is moving to the left with a speed of 2.16 m/s. Suppose the collision is elastic.

Find the magnitude of the final velocity of the 0.141 kg glider.

Find the magnitude of the final velocity of the 0.310 kg glider.

Starting with the 0.31 kg glider...

The conservation of the x-component of momentum:

[tex]m_{A}v_{A1} - m_{B}v_{B1} = m_{A}v_{A2x} + m_{B}v_{B2x}[/tex]

[tex](0.141 kg)(0.74 m/s) - (0.130 kg)(2.16 m/s) = (0.141 kg)v_{A2x} + (0.310 kg)v_{B2x}[/tex]

[tex]-.56526 = (0.141 kg)v_{A2x} + (0.310 kg)v_{B2x}

[/tex]

...I don't know how to simplify that anymore... I suppose what'd be best would be taking [tex](0.141 kg)v_{A2x}[/tex] and trying to get it to just [tex]v_{A2x}[/tex]. But when I multiply everything by 0.141's reciprocal, I still don't seem to get to the right answer.

I get this:

[tex]-.56526(\displaystyle{\frac{1000}{141}}) = (0.141 kg)(\displaystyle{\frac{1000}{141}})v_{A2x} + (0.310 kg)(\displaystyle{\frac{1000}{141}})v_{B2x}[/tex]

[tex]-4.00894 = v_{A2x} + 2.19858v_{B2x}

[/tex]

Which I then add to what I get for plugging in my values to the relative velocity equation:

[tex]v_{B2x} - v_{A2x} = -(v_{B1x} - v_{A1x}) = -(-2.16 m/s - 0.74 m/s) = 2.9 m/s

[/tex]

Adding the two equations:

[tex]-4.00894 = v_{A2x} + 2.19858v_{B2x}[/tex]

[tex]2.9 = -v_{A2x} + v_{B2x}[/tex]

[tex]=[/tex]

[tex]-1.10894 = 3.19858v_{B2x}[/tex]

[tex]v_{B2x} = -.346696 m/s[/tex]

What I'm getting for the final velocity of glider B (the larger glider) is incorrect. According to this, it'll contine on in the direction that it was initally heading... Which makes sense.

What did I do wrong?

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# Another Algebraic Problem Either I Just Don't Know What I'm Doing, Or I'm OutOf It

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