Reletivity: plzz help me asap?

Question

2. How fast would a muon have to be traveling relative to an observer for its lifetime as measured by this observer to be 10 times longer than its lifetime when at rest relative to the observer.

4. A computer in a laboratory requires 2.50 uS(u= Muons symbol) to make a certain calculation, as measured by a scientist in the lab. To someone moving past the lab at a relative speed of 0.995c, how long will the same calculation take?

6. If an electron is speeding down the tow mile long stanford linear accelerator at 99.98% the speed of light, how many meters long is the trip as seen from the perspective of the electron.


8. The tau is the heaviest of all the known leptons, having a mass of 1777 MeV/c². Find the rest energy of a tau in MeVs and Joules. What is the mass of the tau in kilograms? Compare your results with the mass in kilograms of an electron.

Answer 1

2.
√(1 - v^2/c^2) = Tμ/To = 1/10
1 - v^2/c^2 = 1/100
v^2/c^2 = 0.99
v = 0.9949874c

4. 10μs (see above)

6.L = Lo√(1 - v^2/c^2)
L = 2(1,609.344)√(1 - (0.9998)^2)
L = 45.5 m

8. E = mc²
E = (1777 MeV/c²)c²
E = 1777 MeV

You need to have the conversion from MeV to joules, the speed of light in m/s, and the mass of the electron in kg.
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