Time Dilation Question (1 Viewer)

[TeaYarn]

Mesons have a life of 2.2μs. However, mesons formed in the upper atmosphere as air particles are hit by cosmic rays take 16μs to reach the ground. Calculate the speed of the meson?

I have to use this formula right? t = t0/(1-v2/c2)1/2
Please write in the answer what is:
t=
t0=
v=
c=

Thanks

 

[timeflies]

t= 1.6x10^-5s
t0 = 2.2x10^-6s
c = cmon mate, you should know this (speed of light)
v = this what you're tying to find

 

[TeaYarn]

With the velocity, do you have to account for the x speed of light part and divide the other side by it?
Do you think you could write like a worked example?

 

[bokat]

t0=2.2x10^-6
t=1.6x10^-5
v=?
t=t0/sqrt(1-(v/c)^2)
After substiution:
1.6x10^-5=2.2x10^-6/sqrt(1-(v/c)^2)
2.2x10^-6/1.6x10^-5=sqrt(1-(v/c)^2)
1-(v/c)^2=0.01890625
(v/c)^2=0.98109375
v/c=0.99
v=0.99c but c=3x10^8 m/s
so v=2.97 x10^8 m/s

I hope it is clear.

Reza Bokat
Cambridge Coaching