a spin-3/2 particle (25 marks): consider a particle with spin angular momentum j- j. there are four sublevels with this value of j, but different eigenvalues of " 1m 3/2),im = 1/2), im = -1 /2), irn =-3/2). n) show that the raisce i b) what is the lowering operator j? c) what are the matrix representations of j , and which of these operators are hermitian the j, basis? state and show d) check that the state le) _ 2 (v313/2) +11/2)-1-1/2)-v31-3/2)) is an eigeustate of ja with eigenvalue h/2

Asilver dollar is dropped from the top of a building that is 1324 feet tall. use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) determine the position and velocity functions for the coin. s(t) = v(t) = (b) determine the average velocity on the interval [1, 2]. ft/s (c) find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) find the time required for the coin to reach the ground level. (round your answer to three decimal places.) t = s (e) find the velocity of the coin at impact. (round your answer to three decimal places.) ft/s