Special Theory of Relativity question

[Government$]

Homework Statement

A clock moving at velocity u = 3c/5 passes me, sitting at my origin, at t = t' = 0 according to it and my clock. What is its location in my frame when it ticks 1 second in its frame? If it emits alight pulse at that time, at what time t^* according to me will that pulse reach my origin? Use (x, t) for me and (x', t') for clock frame.

I took this form Yale Open Course

Homework Equations

Special Relativity equations

The Attempt at a Solution

I will try to divided this problem into two parts: First one is - what is its location
in my frame when it ticks 1 second in its frame? and second one - If it emits alight pulse at that time, at what time t^∗ according to me will that pulse reach my origin?.

So for the first one i have x=? and that t'=1. I use the lorentz transformation for x point.
x=(x' + ut')/SQRT(1-(u^2)/(c^2)). I am not sure that i can use this formula for this purpose
but if i assume that x' is 0 i get x= ut'/SQRT(1-(u^2)/(c^2)) = 2.25 * 10^8 m
Then i need to find t when light hits my origin ie t^* = t + t'' where t'' is time light takes to travel to my origin in my frame. Perhaps i can get t buy manipulating lornetz equation for t'. Since i have t' and x i can figure out t. t' = (t - (ux/c^2))/SQRT(1-(u^2)/(c^2)) ==>
1 = (t - (ux/c^2))/0.8 ==> 0.8 + 0.45 = t = 1.25. So then i need to find t''. I have no idea to how to find t'' unless to plug int into standard v=s/t formula. If that's the case then c=x/t ==>
t= 0.75 where x is 2.25 * 10^8 m which i found in first part of the problem. So t^* is 2.

I have a feeling that i made a mistake somewhere, possibly at the beginning of the problem where i assumed that x= ut'/SQRT(1-(u^2)/(c^2)) and i am not sure if that's quite right.

 

[Janus]

Looks good to me.