1. We place a muon detector on top of a mountain which is 2000 meters high, and we count the number of muons traveling at speeds of \( v = 0.98c \). Let's assume that during a given interval we count \( 10^3 \) muons.2. Now we move the detector to the bottom or base of the mountain. How long will it take the muon particles to travel 2000 meters at the given velocity?3. According to the muon decay formula above, approximately how many muons are expected to survive from the top to the base of the mountain? Special Relativity: Group ProblemWhen high energy particles called cosmic rays enter the Earth’s atmosphere from outer space, they interact with particles from the upper atmosphere, creating additional particles in a cosmic shower. Many of the particles in the showers are π-mesons which decay into other unstable particles called muons. Muons are unstable and decay according to the radioactive formula:\[ N = N_0 e^{-\left(\frac{\ln(2) \cdot t}{t_{1/2}}\right)} = N_0 e^{-\left(\frac{0.693 \cdot t}{t_{1/2}}\right)} \]Where \( N_0 \) and \( N \) are the number of muons at times \( t = 0 \) and \( t \) respectively. The \( t_{1/2} = 1.52 \times 10^{-6} \) s is called the half-life of muons, which is the time it takes half of the muons to decay to other particles.Answer the following questions and show all of your calculations.

Here we have to use concept of special relativity more specifically length contraction. Due to…

Answered: 2. Now we move the detector to the…

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2. Now we move the detector to the bottom or base of the mountain. How long will it take the muon particles to travel 2000 meters at the given velocity? 3. According to the muon decay formula above, approximately how many muons are expected to survive from the top to the base of the mountain?