3. Muons are charged particles very similar to electrons but more massive. They have an average lifetime of around 2.2 as before decaying into other particles (typically an electron and a few types of neutrinos). Muons are created in the upper atmosphere by cosmic rays. For this problem. we'll say the muons are created about 8 km above the ground. a) Forget about Special Relativity for a moment. Let's just do a calculation using nice and friendly 9A physics (note: the muon's mass is so small there is approximately no acceleration due to gravity). If the muon survives for 2.2 as and travels with a speed of v : 0.997c towards Earth's surface. will the muon reach the ground before decaying? If not. what is the minimum speed the muon needs in order to reach the ground? b) You should have found in part a) that the muon will decay before it reaches the ground. However. experiment has shown that muons D0 in fact reach the ground before decaying. This is considered one of the many experiments that helps to verify special relativity. Redo your calculation from part a) using special relativity to show that muons should reach the ground before decaying. The speed 1' : 0.997(: of the muon is relative to the ground. the given lifetime of the muon of 2.2 as is measured in the inertial frame of the muon. and the distance of 8 km is measured in the inertial frame of the ground. For this part. focus 011 the inertial frame of the ground. For example. how long will the muon live in the inertial frame of the ground? c) Now consider the inertial frame of the muon. In this frame the muon lives for 2.2 as. but if the muon reaches the ground in one inertial frame it must reach the ground in all inertial frames. Again. use your knowledge of special relativity to show that even when considering this inertial frame the muon should still reach the ground