Explination:As Daniel's ball is dropped from the car moving at 40 mph in a horizontal direction, at the time the ball is dropped it is also moving at 40 mph in a horizontal direction due to inertia, a property of mass causing resistance to change, Daniel's ball will continue to move in a horizontal direction even after being dropped along with falling due to gravity. Daniel's ball will then fall in a projectile motion curve of sorts which will cause an overall velocity to not be straight down causing it not to fall to the ground as quickly as Carla's ball.
Carla is not moving. It means that the present energy of the ball is potential energy relative to its height from the ground. There is only a single velocity component on Carla's ball - the vertical component. Therefore, Carla's ball hits the ground first.
Daniel's case is different. The ball travels with two components of velocity - the horizontal velocity and the vertical component. Therefore, the ball's total velocity is a resolution of the two velocities.
Thus, the horizontal component of Daniel's ball follows a projector path and does not fall horizontally. It will touch the ground at some distance after being dropped to the ground.
By conservation of energy, it can climb up to a height equal to that it went down before. However, due to the friction in the machines, the total mechanical energy of the roller coaster will decrease. As a result, the first "hill" of many roller coasters are the highest, but the followings will have decreasing heights.
