Help with length contraction and relativistic momentum please

[shamille]

Homework Statement

A woman is 2.0 m tall and has a mass of 60 kg. She moves past an observer with the direction of the motion parallel to her height. The observer measures her relativistic momentum to have a magnitude of 2.30x10¹⁰ kg·m/s. What does the observer measure for her height?

Homework Equations

L=L_o √1 - (v²/c²)
p=mv/√1 - (v²/c²)

The Attempt at a Solution

I'm pretty sure that these are what the variables are
L_o= 2.0m proper length
p=2.3x10¹⁰
m=60kg
we want to solve for L

my problem is I don't know what v is, if I did i could find it.

I saw that L/L_o = mv/p
so L= L_omv/p right?

but i have no idea how to get v. i haven't had math in a while! any ideas or can you help me? I've tried an online equation solver for didn't work...

 

[Cyosis]

You have p and m so you can solve the momentum equation for v.

 

[shamille]

well i got the answer as 1.24 but i had to use a function grapher and play around with the x and y mins and maxes to find what speed gives a momentum of 2.3E10! which was 0.79C

but i still want to know how to do this because there will be a test and i won't have the internet to help me

thanks in advance

 

[shamille]

You have p and m so you can solve the momentum equation for v.

yes but this is relativistic momentum not p=mv but
p=mv/√(1 - (v2/c2))
and i couldn't solve it for v... is it because I'm crap at math?
can you walk me through how to solve for it? maybe it's more algebra than physics but...

 

[Cyosis]

yes but this is relativistic momentum not p=mv but
p=mv/√(1 - (v2/c2))

There are still only three variables of which you know two.You know how to solve quadratic equations I assume?

$$\begin{align} p=mv \gamma=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}} \\ p\sqrt{1-\frac{v^2}{c^2}}=mv \\ p^2(1-\frac{v^2}{c^2})=m^2v^2 \end{align}$$

Can you solve it from here on?

 

[shamille]

yes! wow as soon as i wrote that last message i figured it out. I don't know where my head was before... and then I used a - instead of +... gahhh

i'm sorry!

but thank you so much

 

[Cyosis]

You're welcome.