Answer:
<em>0.85c </em>
Explanation:
Rest mass of Kaon
= 494 MeV/c²
Rest mass of proton
= 938 MeV/c²
The rest energy is gotten by multiplying the rest mass by the square of the speed of light c²
for the kaon, rest energy
= 494c² MeV
for the proton, rest energy
= 938c² MeV
Recall that the rest energy, and the total energy are related by..
= γ
which can be written in this case as
= γ
...... equ 1
where
= total energy of the kaon, and
= rest energy of the kaon
γ = relativistic factor = ![\frac{1}{\sqrt{1 - \beta ^{2} } }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%7B1%20-%20%5Cbeta%20%5E%7B2%7D%20%7D%20%7D)
where ![\beta = \frac{v}{c}](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20%5Cfrac%7Bv%7D%7Bc%7D)
But, it is stated that the total energy of the kaon is equal to the rest mass of the proton or its equivalent rest energy, therefore...
=
......equ 2
where
is the total energy of the kaon, and
is the rest energy of the proton.
From
=
= 938c²
equ 1 becomes
938c² = γ494c²
γ = 938c²/494c² = 1.89
γ =
= 1.89
1.89
= 1
squaring both sides, we get
3.57( 1 -
) = 1
3.57 - 3.57
= 1
2.57 = 3.57
= 2.57/3.57 = 0.72
= 0.85
but, ![\beta = \frac{v}{c}](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20%5Cfrac%7Bv%7D%7Bc%7D)
v/c = 0.85
v = <em>0.85c </em>