Two students accept the following challenge: to hit a pendulum with a bullet fired from a spring$-$loaded gun while the bullet is at the top of its trajectory and after it has passed through the opening of a hollow cylinder as it rolls down a ramp. $($See diagram below, which is not to scale.$)$

They began by determining that the ball rose $222$ cm when fired vertically. Then, they placed the axis of the gun perpendicular to the plane of the ramp, opposite its center and inclined at $20^($@$).$ The ball was then $125$ cm to the left of the ramp and $9\mathrm{.}6$ cm above the table. Subsequently, they determined where to place the pendulum $($ x$,$y coordinates$)$ and calculated the approximate time between the moment of firing and the start of the rolling of the hollow cylinder so that the ball was opposite the center of the disk at the right time. Determine:

a$)$ the speed with which the bullet is fired, $($Answer:$6\mathrm{.}60$m$/$s$)$ Solved

b$)$ the height of the ball when x$=0,($Answer:$0\mathrm{.}352$m$)$ Solved

c$)$ the place where the pendulum should be placed so that the ball hits its center, $($ Answer: x$=0\mathrm{.}177$ m and y$=0\mathrm{.}356$m$))$ Unsolved

Hello, I would like to know how to find the answer to c$)$ please

Thank you