Consider a spin-1/2 particle with a magnetic moment. At time t = 0, the state of the particle is 0c1t = 029 = 0 +9n with the direction nn = 1n x + yn2 > 12. The system is allowed to evolve in a uniform magnetic field B = B0zn. What is the probability that the particle will be measured to have spin up in the y-direction after a time t?

Ajogger accelerates from rest to 4.86 m/s in 2.43 s. a car accelerates from 20.6 to 32.7 m/s also in 2.43 s. (a) find the magnitude of the acceleration of the jogger. (b) determine the magnitude of the acceleration of the car. (c) how much further does the car travel than the jogger during the 2.43 s?

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

What is the order of the moon, earth, and sun in a lunar eclipse and a solar eclipse?