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The Historical Answer of Huai 'an's Second Mode
Solution:

(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.