(1) Draw the trajectory of the ball in the magnetic field B 1, as shown in the figure.
R 1-h=R 1cos60,R 1=2h
By qvB=mv2R and B 1=2B2.
It is known that R2=2R 1=4h.
By qv (2b0) = mv2r 1
Get v = 4qb0hm
According to the symmetry of motion, the distance of PQ is
l = 2(r 2 sin 60-r 1 sin 60)= 23h;
(2) The time from p to q is t = t13+2t23 =132π mq (2b0)+232π mqb0 = 5π m3qb0.
The speed of uniform motion of astronauts is V = LT = 63QB0H5π m.
According to the law of conservation of momentum, MV-mv=0.
You can get the astronaut's mass m = 10π m33.
Answer: (1) The distance between PQs is 23.