- #1
Gregorski
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Homework Statement
This is new for me, so forgive me my clumsiness. I am working on the following problem:
A particle p is moving with a velocity v1 = c (speed of light) towards an object q, which is moving in the same direction with the speed v2, where v1>v2. Now, v2 is a function of the distance r between p and q. I need to find the time when p "catches up" with q.
Homework Equations
v2(r)= v0hr, where h - the Hubble constant, v0 - initial velocity, and r - distance between p and q
The Attempt at a Solution
Particle p will "catch up" with q when the distance between them is 0, so we have:
r - s =0 and r = s (1)
v2(r)= v0hr
Differential equation:
ds/dt = v0hr
Separating variables:
ds/r= v0h dt
Integrating:
log r = v0ht + c
r = ev0ht+c
r = ecev0ht
ec=R
r=Rev0ht
Plugging into (1)
Rev0ht = v1t
I am not sure how to proceed from here or if any of it makes sense.