# Not able to clearly understand the text of a problem [closed]

I've not clearly understood what it's meant by the text of this problem. To me, it seems that I have to show why an object travels AB in less time than ACB. However, if an object travels from A to C, why doesn't it stop at C?

## closed as off-topic by Bob D, John Rennie, Bill N, Kyle Kanos, tpg2114♦May 11 at 7:03

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• Would help if I fully understood which is B and C... – Rick May 5 at 13:06
• The book doesn't show. If we consider the triangle in the figure, i think A is the top-left vertex, B is the top-right vertex and C the remaining vertex – AleQuercia May 5 at 13:18
• You have to prove why an object travels faster along ACB than along AB according to the text, which says, "Prove that wherever pt. C is chosen on the arc AB, an object will always get from A to B faster along the slopes ACB than along the original slope AB." If an object travels from A to C, it wouldn't stop at C because of the inertia of motion. – Tapi May 5 at 13:24
• Okay thanks. So is the inertia what i didn't understood. How can i understand deeply why an object at C doesn't stop ? – AleQuercia May 5 at 13:41
• No change in speed means there must be an elastic collision when it hits C. – Cuspy Code May 5 at 13:54

Mathematically, if you take the acceleration of the object to be 'a', and take its vertical component, it turns out to be $$a cos\theta$$, $$\theta$$ being the angle AB/AC makes with the normal (parallel to the side of the container). Now, $$cos\theta$$ is more for AC than for AB, because $$cos \theta$$ decreases as $$\theta$$ increases. Hence, $$a cos\theta$$ is more for AC, than for AB. Thus, acceleration is more for AC, making the journey through ACB faster than through AB.