(1) When the ball is on an inclined plane, it is obtained from Newton's second law: GSIN 37- micron GCOS 37 = Ma.

Solution, the acceleration of a and b: AA = AB = GSIN 37? μgcos37 =2m/s2，

The time from ball a to point c is sa = h1sin37 =12aata2? tA=2h 1aAsin37 =3？ s，

The time from ball B to point C is: Sb = H2SiN37 = 12ABTB2? tB=2h2aBsin37 = 1？ s，

The balls A and B will not collide on the inclined plane, and the longest t is: t = ta-TB = 2s；;

(2) The speed of the ball from point A to point C is vA=aAtA=6m/s,

Let a catch up with b at time t, then: vA(t? tA)= 12at2，

T≤vAa，

Solution: a≤ 1m/s2,

That is, b-ball acceleration a? The maximum shall not exceed1m/S2;

Answer: (1) In order to ensure that ball A and ball B will not collide on the inclined plane, the maximum length of T should not exceed 2s.

(2)B ball acceleration a? When the maximum cannot exceed 1m/s2, ball A may catch up with ball B. 。