A ball being projected from a funnel sliding down a smooth inclined surface. The velocity of the ball relative to the funnel is initially normal to the inclined surface. The ball drops in to the funnel because it shares the same motion as the funnel in a direction parallel to the plane.

In a direction parallel to the plane the conditions of motion for the ball and the funnel are same. The accelertion of the funnel and and the ball parallel to the plane are equal to g sinθ and velocity of the ball and the funnel parallel to the plane are same at the moment the ball is projected and they subseuently increase at the rate of g sinθ(red vectors are always equal).

The ball in addition has a velocity (black vector) normal to the plane and an acceleration of g cosθ directed towards the plane. While velocity of the ball normal to the plane decreases to zero, reverses and then increases, the ball and funnel are travelling the same distance parallel to the plane.

There is no motion relative to the funnel in a direction parallel to the plane, because in that direction the conditions are same.

In a direction parallel to the plane the conditions of motion for the ball and the funnel are same. The accelertion of the funnel and and the ball parallel to the plane are equal to g sinθ and velocity of the ball and the funnel parallel to the plane are same at the moment the ball is projected and they subseuently increase at the rate of g sinθ(red vectors are always equal).

The ball in addition has a velocity (black vector) normal to the plane and an acceleration of g cosθ directed towards the plane. While velocity of the ball normal to the plane decreases to zero, reverses and then increases, the ball and funnel are travelling the same distance parallel to the plane.

There is no motion relative to the funnel in a direction parallel to the plane, because in that direction the conditions are same.