Physics proportion problem...

[BestDoctorEver]

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A stone of mass m is dropped from a height h. If air resistance is negligible, which one of the following statements is true concerning the stone as it strike the ground?

A. Its speed is proportional to h
B. Its speed is proportional to h^2
C. Its kinetic energy is proportional the h
D. Its kinetic energy is proportional to h^2


I know that C is the correct answer...But I was wondering why B is not a good answer as well since the speed V = sqrt(2gh) and if h is squared then V will be proportional to h. I am assuming the object was dropped from rest.

 

[milski]

Because just like you said, V is proportional to the square root of h. You cannot just square h and plug it in - that's not a distance anymore.