Two particles a and b have velocities 3î and 4î + ſ respectively. (i) find rbiat), the position of b relative to a for all t given that rb|a(t = 0) = –2î – 6ſ. 15 marks (ii) show that a and b are closest together when t = 4 and hence find the shortest distance between them.

Acyclotron is used to produce a beam of high-energy deuterons that then collide with a target to produce radioactive isotopes for a medical procedure. deuterons are nuclei of deuterium, an isotope of hydrogen, consisting of one neutron and one proton, with total mass 3.34×10−27kg. the deuterons exit the cyclotron with a kinetic energy of 6.40 mev .a-what is the speed of the deuterons when they exit? b-if the magnetic field inside the cyclotron is 1.25 t, what is the diameter of the deuterons' largest orbit, just before they exit? c-if the beam current is 350 μa how many deuterons strike the target each second?