BR Physics Ch. 1 Passage I Answer explanation

[ktal]

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Hello everyone!

I started studying for the MCAT today, and did Ch 1 of BR Physics. I was going over the answers, and for Passage I Q#3 they derive equations and then they do the following:

RD= VoB sqrt(2h/(1/2gB)) = sqrt(2) VoB sqrt(2h/gB) = sqrt (2) RB

SO.. I understand how they derive the first part of the equation, but I cannot see for the life of me where they go from the first part to the second! I mean, I do know about playing around with equations, but I don't see how they get that sqrt(2) and they get rid of the 1/2gB to go to just gB for the denominator of the first sqrt.
Please, if someone knows what I am talking about, and see how they got to that answer, please enlighten me. Thanks!!

Sorry it's a stupid question.. =/
Thanks for the help.

 

[BerkReviewTeach]

Hello everyone!

I started studying for the MCAT today, and did Ch 1 of BR Physics. I was going over the answers, and for Passage I Q#3 they derive equations and then they do the following:

RD= VoB sqrt(2h/(1/2gB)) = sqrt(2) VoB sqrt(2h/gB) = sqrt (2) RB

SO.. I understand how they derive the first part of the equation, but I cannot see for the life of me where they go from the first part to the second! I mean, I do know about playing around with equations, but I don't see how they get that sqrt(2) and they get rid of the 1/2gB to go to just gB for the denominator of the first sqrt.
Please, if someone knows what I am talking about, and see how they got to that answer, please enlighten me. Thanks!!

Sorry it's a stupid question.. =/
Thanks for the help.

This is EXACTLY why I love the newer version of the physics book and not the one you are using. In the new book, they include an intuitive apporach as well as the math. I copied the intuitive part for you.

• "You could also have also solved this question intuitively by noting that both stones have the same initial speed in the x-direction, but Stone D stays in the air logner than Stone B (due to reduced gravity). We know that the stone in Trial D will travel farther than the stone in Trial B, so choices C and D are eliminated. They start from the same height, which relates to flight time by a square root factor, so there must be a square root in the relationship. This eliminates choice A. Only choice B remians standing, so it must be the best answer."

As for the math, you need to divide the RD by RB.

RD/RB = voD x sqrt(2h/gD)/voB x sqrt(2h/gB)​

Because voD = voB, we get:

RD/RB = sqrt(2h/gD)/sqrt(2h/gB)​

Because they are both dropped from the same height, we get:

RD/RB = sqrt(1/gD)/sqrt(1/gB) = sqrt(gB/gD)​

Because gB = 2gD, we get:

RD/RB = sqrt(gB/gD) = sqrt(2gD/gD) = sqrt2​

I hope this helps.

The point in many of the answer explanations in the new physics book is that you should be using intuition more than math and visualization more than equations, although equations are excellent for varifying relationships.