The muon is a particle that has the same charge as an electron, but at rest is 207 times as massive. unlike electrons, muons are unstable and decay in 2.2 hs, producing an electron (and a neutrino which has almost zero mass.) muons are created high above the earth when cosmic rays (high energy protons or nuclei arriving from space) collide with atomic nuclei of nitrogen and oxygen found in the atmosphere. the muons approach the earth with an astounding velocity of 0.995 c. the earth's magnetic field deflects some of the cosmic rays, and it also redirects the muons. a laboratory high on mt washington, 1900 m above ground in new hampshire, where the local magnetic field is 15 x 10-6t directed north, made important measurements of this muon "rain" in 1963 that confirmed the theory of special relativity _7. in the muon's frame of reference (a) their lifetime is shorter than 2.2 us (b) their lifetime is longer than 2.2 us (c) the distance to the earth is longer than expected (d) the distance to the earth is shorter than expected (e) more than one of the above _8. in the earths' frame of reference (a) their lifetime is shorter than 2.2 us b) their lifetime is longer than 2.2 hs (c) the distance to the earth is longer than expected (d) the distance to the earth is shorter than expected (e) more than one of the above 9. a laboratory at the foot of mt washington and the lab at the top of mt washington agree that they observed 2 muons decay at exactly the same time. to the muons (a) this is also correct (b) the muon at the top decayed before the mon at the ground (c the muon at the ground decayed before the muon at the top. 10. the cosmic rays would be (a) deflected in the same direction as the muons (b) deflected in the opposite direction as the muons (c) deflected at 90° to the muons (d) not deflected at all 11. if it were not for the earth's magnetic field, the muons would have landed (a) to the west of new hampshire (b) to the east of new hampshire (c) exactly where they did land (d) north of new hampshire (e) south of new hampshire _12. the high velocity of the muon changes what an outside observer measures for (a) its mass, only (b) its charge, only (c) both its mass and its charge (d) neither its mass nor its charge

Red’s momentum vector before the collision is green’s momentum vector after the collision. question 1 options: equal to shorter than longer than question 2 (1 point) saved since green bounces off red, this must be an collision. question 2 options: explosion elastic inelastic question 3 (1 point) red transfers of its momentum to green during the collision. question 3 options: none all little most question 4 (4 points) why does red transfer all its momentum to green? back up your answer with information from the simulation. write at least 2 sentences. question 4 options: skip toolbars for . more insert actions. more text actions. more paragraph style actions. question 5 (1 point) now make red much heavier than green. answer the questions below to describe how both red and green behave after the collision. question 5 options: slowed down sped up kept the same velocity question 6 (1 point) green sped up during the collision as it question 6 options: gained momentum from red lost momentum to red maintained a constant momentum. question 7 (1 point) after the collision . . question 7 options: both green and red moved to the right. both green and red stopped as they have lost all momentum. red stopped and green moved to the right. red bounced off green and went to the left. green moved to the right. question 8 (4 points) only some of red’s momentum was transferred to green. why did this occur? back up your answer with information from the simulation. write at least 2 sentences. question 8 options: skip toolbars for . more insert actions. more text actions. more paragraph style actions. question 9 (1 point) now make red much lighter than green. answer the questions below to describe how both red and green behave after the collision question 9 options: green sped up after the collision therefore it must have gained momentum. green sped up after the collision therefore it must have lost momentum. green slowed down after the collision therefore it must have gained momentum. green slowed down after the collision therefore it must have lost momentum. question 10 (1 point) since green gained momentum, red had to have momentum because you cannot create or destroy momentum. question 10 options: gained lost kept the same amount of question 11 (1 point) since green was so much and harder to move, it caused red to bounce back to the left giving red . question 11 options: heavier . . . . positive lighter. . . . negative lighter. . . . positive heavier . . . . negative question 12 (4 points) now, click on more data at the bottom of the sim. play with different numbers for the masses and starting velocities. you can even make the starting velocities negative! tell me one thing you discovered by adjusting the speeds and masses. write at least 2 sentences. be specific and use words like velocity, momentum, mass, increased, decreased, etc. 13. true or false: when red and green collide, they stick together. question 13 options: true false question 14 (1 point) the velocity of red & green after the collision is the velocity that red started off with. question 14 options: larger than smaller than equal to question 15 (1 point) the velocity after the collision was less because the mass has question 15 options: stayed the same decreased increased question 16 (1 point) the momentum before the collision was the momentum after the collision. question 16 options: larger than smaller than equal to conclusions question 17 (4 points) how are elastic and inelastic collisions different? give two or more ways. your answer should have at least 2 sentences. question 18 (4 points) give an example of a collision in real life. use the law of conservation of energy to describe the transfer of momentum. be sure and discuss the momentum before and after the collision occurs. you will need at least 3 sentences to thoroughly answer this question.

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

What would be the radius of the earth if it had its actual mass but had the density of nuclei? express your answer to two significant figures and include the appropriate units.