# Relative momentum, Rest Energy, Kinetic energy and speed of a proton

1.
a) A relativistic proton has a momentum of 10x10^-18 kg*m/s. The rest energy of a proton is 0.150nJ. The kinetic energy of the protoon
b) In this situation the speed of the proton is?

2. E=MC^2
P= MV/sqroot(1-(v^2/c^2)
K=[MC^2/ sqroot(1-v^2/c^2)]-[mc^2]

3. The algebra in this problem. First I found the mas of the proton by using its rest mass
0.150nJ/c^2=1.6x10^-27kg

now I am trying to use the relativistic momentum to find the velocity of the object this is where my algebra is confusing. I see that v is the variable to solve but I can't get the V by itself. can anyone help me with the algebra. I do know since I will b solving for velocity in term of c then the velocity under the square root can be looked at as just v^2 instead of v^2/c^2. Even after that I tried to get rid of the square to get v in in one side and that didn't work becuase the v ended up canceling each other out any ideas on how to do this? Once I find out the velocity the Kenetic energy will be very easy to solve.