Particle decaying into two daughter particles - special relativity

[physconomics]

Homework Statement

A D meson decays into a K and pi-meson. Calculate energy and velocity of pi meson

Relevant Equations

E^2 = p^2c^2 + m^2c^4
Four vectors
rest mass of D = 1.86GEV/C^2
K = 0.5GEV/C^2
PI = 0.13GEV/C^2

Right, so I thought I'd done this correctly but clearly not because my velocity is greater than the speed of light, where have I gone wrong?

P = (M, 0, 0, 0)
p₁ = (E1, p1x, p1y, p1z)
p₂ = (E2, p2x, p2y, p2z)
P = p₁ + p₂
p₂ = P - p₁
square each side
to get (p₂)² = P² - 2Pp₁ + p₁²
therefore
(m₂)² = M² - 2ME₁ + m₁²
So E₁ = (M² - m₁² + m₂²) / (2M)
which gives 0.867GeV

then
p₁ = sqrt(E₁² - m₁²) = 1.372x10^-10
then because p₁=ymv, v = 8.90x10^16
where y = 0.867/0.13

Thank you!

 

[Abhishek11235]

p1 = sqrt(E12 - m12) = 1.372x10^-10
then because p1=ymv, v = 8.90x10^16
where y = 0.867/0.13

Can you explain this?