Question

The kinetic energy of a proton is half its internal energy. What is the proton's speed?

Kinetic energy is (Yu - 1) (mp) (c)^2

= 1/2 (mp) (c)^2

Yu = 1.5



Yu = 1/(square root) 1 - (u/c)^2

1/(square root) 1 - (u/c)^2 = 1.5

u= 0.745c

How do I solve for u? I'm extremely confused on how to do this. I know you square 1/(square root) 1 - (u/c)^2 to both sides esp. 1.5 to get rid of the square root. But up to there I'm confused to how to solve for u

Answer 1

1/√(1-(u/c)^2) = 3/2
√(1-(u/c)^2) = 2/3
(1-(u/c)^2) = 4/9
(u/c)^2 = 5/9
u/c = √5/3 = .745
u = .745c

Answer 2

thank you