I was doing some conceptual problems quickly before moving on to the numerical stuff when I glanced at this answer given in the solutions manual, and it surprised me:(adsbygoogle = window.adsbygoogle || []).push({});

Which object has greater speed at the bottom of its fall, object A of mass m dropped freely from height h or object B of mass m moving down an incline (no friction) from height h?

The manual says A. I googled around and found different people saying different things on this! I thought the answer was just that they have the same speed.

The manual gave this as its explanation: for A, v = sqrt(2gh), whereas for B, v = sqrt(2g(sinθ)h). Therefore, A is greater.

One of the online answers gave this: both A and B start with PE = mgh; so, at the end, all PE is now KE; so, KE = mgh = 1/2(mv^2); so both A and B have the same v, namely v = sqrt(2gh).

My analysis is that the manual mistakenly gives g(sinθ) for the acceleration on the incline. Maybe they were thinking of the force component?

I’d be grateful for help getting clear on this.

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# B Velocity after Free Fall and after Motion down an Incline

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