Physics Question on kinetics/momentum (Last Attempt Need Help)
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Physics Question on kinetics/momentum (Last Attempt Need Help)

[From: ] [author: ] [Date: 12-05-17] [Hit: ]
Im not sure if this is right, but thats the answer I got using the method I came up with.......
A proton has 1836 times the rest mass of an electron. At what speed will an electron have the same momentum as a proton moving at 0.0088c? v=______c
I first started using m1v1=m2v2 but that is wrong
tried 1/sqrt(1836)*.0088c but was also wrong. I am just so lost and frustrated on this question. I ask of you for your assistance. If you could please explain your process so I can better understand the material I would be very grateful. Thank You for your time.

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p = γmv

p is momentum, γ is the Lorentz factor, m is the rest mass, v is the velocity

For the proton:

γ = 1 / (1 - (v / c)^2)^(1/2)) = 1.0000387

Set the momentum of the proton and electron equal to each other:

p = (1.0000387)(1836m)(0.0088c) = γmv ---> m's cancel

(1.0000387)(1836)(0.0088c) = γv

γv = 16.1574c

Plug in what we know γ is equal to:

(1 / (1 - (v / c)^2)^(1/2)))v = 16.1574c

Solve for v: (I used my TI-89 calculator)

v = 0.99809c

I'm not sure if this is right, but that's the answer I got using the method I came up with.
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