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DunWorry
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Homework Statement
a D meson is at rest and decays into a Kaon and a Pion. The Kaon moves with speed 0.867c and has a mass of 0.494 GeV/C^2. The pion has a mass of 0.140 GeV/C^2. use conservation of momentum to calculate the speed of the Pion.
Homework Equations
Relativistic Momentum P = [itex]\gamma[/itex]mV
where [itex]\gamma[/itex] is [itex]\frac{1}{\sqrt{1 -\frac{v^{2}}{c^{2}}}}[/itex]
The Attempt at a Solution
So if the D meson is initally at rest, initial momentum = 0, which means
[itex]\gamma[/itex][itex]_{v1}[/itex]m[itex]_{1}[/itex]v[itex]_{1}[/itex] = [itex]\gamma[/itex][itex]_{v2}[/itex]m[itex]_{2}[/itex]v[itex]_{2}[/itex]
Where particle 1 is the Kaon and particle 2 is the Pion, we want the speed of Pion so we solve for v[itex]_{2}[/itex]
After some rearrangement I got v[itex]_{2}[/itex][itex]^{2}[/itex] = [itex]\frac{1} {\frac{m_{2}^{2}}{(\gamma_{v1}m_{1}v_{1})^{2}} + \frac{1}{c^{2}}}[/itex]
After plugging in the numbers m2[itex]^{2}[/itex] = ([itex]\frac{0.140x10^{9}}{(3x10^{8})^{2}}[/itex])[itex]^{2}[/itex]
and m1[itex]^{2}[/itex] = ([itex]\frac{0.494x10^{9}}{(3x10^{8})^{2}}[/itex])[itex]^{2}[/itex]
and [itex]\gamma[/itex][itex]_{v1}[/itex] = [itex]\frac{1}{\sqrt{1 - 0.867^{2}}}[/itex]
I get an answer faster than light, where have I gone wrong?