Ball Rolling Down A Ramp [Science Challenge Question]

[CallMeShady]

Homework Statement

Hello Physics World,

This is a question that was presented in my High School Science Challenge by a teacher. It is sort of a brain teaser and we will be told the answer to it by next week. However, I was wanting to know your input.

So, looking at the image above, which route will take less time for the ball to reach the bottom?

a) Route A
b) Route B
c) Both routes will take the same amount of time.

NOTE: Please ignore the slope of the route B - that was drawn free-handed. And I also must say that this question is rather ambagious since no additional information was given (like friction values, ramp length, etc.).

Homework Equations

None given.

The Attempt at a Solution

I believe that the answer is c) because taking route A would mean that the ball is rolling down at a constant acceleration (if friction was neglected) and route B would have an increasing acceleration once it goes down the ramp (due to the hollow shape on the ramp) and as it goes back up the hollow shape, the ball will decelerate; so while taking NET distance with time, the time for both routes might be the same.

 

[danielh88]

I believe the answer to this is C).
Imagine the point where the two point separateis point A.
Also imagine the point where they reunite is point B.

In route A, the ball is rolling at a constant acceleration.
In route B, the ball increases acceleration at point A and decreases acceleration to meet at point B.

At that point We can take the average slope from point A to point B. Which is a straight line.

Therefore since they meet a point B, the instantaneous acceleration at point B is the same in route A and route B. so time will be the same.

 

[CallMeShady]

Any other community input please? The response above was by a classmate of mine.