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# (I) What is the momentum of a proton traveling at $v=0.75 c ?$

## $5.7 \times 10^{-19} k g . m / s$

### Discussion

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##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Farnaz M.

Simon Fraser University

### Video Transcript

our question asked us to find the mo mentum of a proton that's traveling at a speed of V equals 0.75 times the speed of light. Okay, so right now what we're given here in our question, that's V equals 0.75 times the speed of light on the Madison. A proton is 1.67 times 10 to the minus 27 kilograms and the speed is equal to three times 10 to be eight meters per second. So then mo mentum relativistic lee is equal to gamma times, the mass times the velocity. So this is equal to the mass times the velocity and then gamma is one over the square root of one minus V squared over C squared. So Gammas one over a squared of one minus B squared over C squared. Okay, so then if you plug in all the values that we have for the mass for the velocity for the speed of light, this comes out to be 5.7 three. That's seven area 5.7 times 10 to the minus 19. The units on this are kilograms climbs meters per second box set in is our solution

University of Kansas
##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Farnaz M.

Simon Fraser University