AAMC 8 Physics Question

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eybc20

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Hey everyone,

I had a question about AAMC 8 Physics. The question is:

(19) When designing his experiment, Galileo could have allowed spheres to drop from a height of 10 m rather than using the 10-m inclined plane described in the passage. The main advantage to using the inclined plane is that on the inclined plane the:

A) Final velocity of a sphere is smaller
B) Final velocity of a sphere is larger
C) Spheres take longer to reach the bottom
D) Spheres take less time to reach the bottom

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The correct answer is C. I got it right, but not for the right reasons- I actually thought that the velocity of the rolling ball would be smaller at the end of the inclined plane than if you had dropped it vertically, and thus would take longer and be easier to measure.

My reasoning is: a 10-m inclined plane, unless you tilt it vertically, will never have a height of 10 m. Therefore, according to mgh = (1/2)mv2, the final velocity for the inclined plane will always be smaller because its height can never reach the magnitude that the vertical 10 m drop will have. However, AAMC is saying that the final velocity between the drop and the inclined plane is the same. What's wrong with my reasoning?

Thanks in advance! I appreciate any help I could get.

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That wasn't the main advantage. The main advantage is it takes longer to travel to the ground and he used the data as another way for confirming his gravity theory.
 
Height refers to the vertical component of the inclined plane, not the hypotenuse of the inclined plane as you are inferring; if you release a sphere from the top of an inclined plane with a height of 10 m, it will have the same final velocity as a sphere dropped straight down from a height of 10 m because of the law of conservation of energy in an isolated system (Potential Energy = Kinetic Energy). However, the time it takes the ball to travel down the hypotenuse of the inclined plane will be greater than the time it takes to be dropped straight down because the distance the ball travels on the inclined plane will be greater than 10 m distance covered when dropped through the air.

TL;DR: A 10 m inclined plane has a height of 10 m.
 
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