Answer
(a) Straight vertical line.
(b) Part of the parabola.
Work Step by Step
(a) The child and the scoop of ice cream had zero relative velocity between each other. When the scoop falls, it will experience the gravitational acceleration which is strictly vertical but there will still be no relative motion in the horizontal direction so the scoop will appear to be in free fall and the path would be a vertical straight line.
(b) To the parents, the scoop will have the initial velocity that is in horizontal direction equal to the velocity of motion of the pony, but it will start accelerating downwards with the gravitational acceleration so the motion will look like the motion of a horizontally fired projectile, i.e. a part of the parabola.
