Derive time for relativity (i know how but not sure what to do i got a idea

[seto6]

Homework Statement

Homework Equations

equation 37.23 37.30 are the following

37.23
x'=gama(x-vt) x= gamma(x'+vt')
t=gamma(t-vx/c²) t'=gamma(t'+vx'/c²)

37.30
u'=(u-v)/(1-uv/c²) u=(u'+v)/(1+uv/c²)

The Attempt at a Solution

i tried the following...

since d=vt... i solved fot t=d/v

so (x'/u')=gama(x-vt) /((u-v)/(1-uv/c²)) but its not working can someone tell me where I am going wrong

 

[seto6]

but... now i see that i would have to derive instead dividing

like...dx'/du'

but I am not sure how..

 

[seto6]

any1

 

[seto6]

could soneone help me set up dx/dv pls

 

[Gear300]

If you know the Lorentz relation for the length contractions, you can substitute one into the other and solve for a relation between t and t' (you should also end up with a spatial dependence in there).

For the second part, you would not expect spatial contractions along the y-direction since it is orthogonal to the direction of the relative velocity. Though, you could still expect a time dilation; so the derivation for u_y to u_y' would be the same way as done with u_x to u_x', except that you do not need to take into account a length contraction for the y-direction.

 

[seto6]

can you tell me what this is Lorentz relation for the length contractions..mean the formula