Speed of a particle...physics help 2-11-9

Question

What is the speed of a particle whose kinetic energy is equal to three times its own rest energy?

Answer 1

So,it must be in a height,then WH=1/2MV^2,  MGH=1/2MV^2

3(9.8)H=1/2V^2,  V^2=58.8H ,V=7.668XH

Answer 2

Rest (mass) energy Em = m0c^2 (ref. 1)

KE = (m-m0)c^2 (ref. 1)

If KE = 3Em, m-m0 = 3m0 ==> m = 4m0 ==> γ = 4 (ref. 2)

Then β = sqrt(1-1/γ^2) = 0.968245836551854,

v = βc = 290272799.288147 m/s (answer),

where c = 299792458 m/s