Relativity Problem: Muons Traveling at .99c Towards Earth

[Wannabeagenius]

Hi All,

I'm trying to do a Relativity problem and I'm having trouble.

There is a detector on a balloon at 2000 meters above the Earth that in one hour has detected 650 muons that normally have a half life of 1.5 microseconds. They are traveling at .99c towards the earth. How many are detected at the Earth in one hour.

Now due to time dilation, I get 10.633 microseconds for the half life relative to ground observers. That seems pretty reasonable.

Now I figure that all I need to know is how long it takes for them to travel 2000 meters and that seems to be a classical calculation. Time =2000 meters/.99c but my answer is way off.

Am I approaching this correctly? I am wondering about calculating the time it takes the muons to reach the ground in a classical manner?

The book answer is 420 but I get over 600.

Thank you,
Bob

 

[Dick]

I don't see that you've done anything wrong so far. How did you finally get to 'over 600'?