High Road, Low Road

Which road is faster? A kinematics concept Puzzler.

high low road

What it shows:

Horizontal and vertical motions are independent of each other.

How it works:

Two balls, starting with the same initial horizontal velocity, take two different paths: the one taking the high road is simply a straight horizontal path; the one taking the low road rolls down into a valley, follows a short straight horizontal stretch, and then back up again to the original height. The horizontal distance traveled by each is the same, but the low road is obviously a longer path.

Presented as a concept question (puzzler), students are asked to predict which ball wins the race. Most students will think the high road, because it's shorter. Students who already know about conservation of mechanical energy usually think it's a tie. The class is always surprised to see that the longer low road wins. Having explained the concepts to the class, the students are asked to predict what will happen with an even lower road which has no flat section at the bottom. Most fail to apply the concepts correctly to this situation and think that surely the high road will win this time. Wrong again! Indeed, a race between the two low roads shows that the lower of the two wins.

Setting it up:

The two billiard balls are held at the same height and then released simultaneously to roll down a short incline. This gives them the same initial horizontal velocity when they reach the flat section of the track.


This is a terrific concept question/demonstration. Being counter-intuitive, it never fails to pique the students' interest and ask more questions. A favorite question which you should be prepared to answer is, "How low can you make the road and still have it work?"