00:01
So the gist of this problem is that you have a tau lepton.
00:03
It's moving at a relativistic speed.
00:05
So from the laboratory frame of reference, it's time dilated.
00:09
So it has proper time in its rest frame.
00:14
But because of the time dilation, it lasts longer in the laboratory frame.
00:18
Travel some distance l in the laboratory frame, it wants you to find that distance.
00:23
So the way you go about solving this problem is it gives us the kinetic energy.
00:28
And implicitly, you have to look it up.
00:30
Gives you the proper time and the mass of the tile lepton.
00:35
So the heuristic here is you use k to find gamma, then you use gamma to find delta t.
00:54
Yep.
00:56
And then you also use gamma to find the speed of the lepton.
01:07
And then for v, you know those two, then you can use that to find l, because l is defined in terms of those things.
01:25
V is the speed in the laboratory frame.
01:31
So we know that the kinetic energy is gamma minus 1 times mc squared.
01:45
So let's see, that is, how does i want to write this? i can't go to g -d -d -by -bye.
02:05
Okay, so i'm going to do this, k over mc -squared equals gamma -minus 1.
02:14
Therefore, gamma equals k -m -c -squared plus 1.
02:23
So that's 950 m -ev over 1 -77.
02:32
On m .e .v.
02:36
Plus one.
02:41
So that ends up working out to being gamma is 1 .535...