Should the teacher draw an arc ab? Here's the thing. The radius of particle motion is mv/qB=0.06, so the circle where the trajectory arc of particle motion is located is larger than the range of magnetic field, and the initial velocity of particle remains unchanged. Therefore, the motion time of the particle is required to be the longest, that is, the maximum distance of the particle motion in the magnetic field, so as long as the magnetic field cuts the trajectory circle of the particle, the maximum arc length can be obtained. The longer the arc, the longer the corresponding chord, and the longest chord is the diameter ab. Therefore, when the motion time is the longest, the trajectory of particles is an arc connecting ab endpoints.

Finding the trajectory is half the battle, and then the math problem in junior high school. First, you draw a particle motion circle roughly. Let its center be C, and its radius is R=0.06 and chord length ab is 2r=0.06. It is concluded that abc is a regular triangle and the central angle ACB is 60 degrees, so the movement time is tmax=(60 degrees /360 degrees) * period. The period T=2* pi *R/v0, and the result will be obtained immediately.