Suppose a $6\mathrm{.}0$ gram marble with a diameter of $1\mathrm{.}65$ cm$,$ made from solid glass, rolls down a curved ramp, as shown in the figure.$$ The marble starts at rest at the top of the ramp and rolls without slipping.$$ The ramp has a total height of $0\mathrm{.}70$ meters, and the bottom of the ramp is $1\mathrm{.}20$ meters above the floor.$$ The very end of the ramp has a slight downward angle, $15$ degrees below the horizontal.$$ At what horizontal distance should a student place a bucket that is $25$ cm tall and has a diameter of $10$ cm at the top of the bucket, to catch the marble?$$