TBR Physics Passage 1 Question 2

[golgiapparatus88]

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This question is really throwing me off.. The answer description is on page 51 of the Physics 1 Berkeley Review book.

For those of you who don't have the book, you must compare the drop time of a stone, one on earth and the other on another planet which has a gravitational acceleration of 5m/s^2. It seems like a basic ratio but the book really thows me off.

With the equation t = sqrt 2h/g you can say t(earth) = sqrt 2h/2g because the other planet is only half. The book than converts this to sqrt 1/2 (2h/g).

How do you go from sqrt 2h/2g to sqrt 1/2 * (2h/g)???

 

[DavidMD2B]

This question is really throwing me off.. The answer description is on page 51 of the Physics 1 Berkeley Review book.

For those of you who don't have the book, you must compare the drop time of a stone, one on earth and the other on another planet which has a gravitational acceleration of 5m/s^2. It seems like a basic ratio but the book really thows me off.

With the equation t = sqrt 2h/g you can say t(earth) = sqrt 2h/2g because the other planet is only half. The book than converts this to sqrt 1/2 (2h/g).

How do you go from sqrt 2h/2g to sqrt 1/2 * (2h/g)???

If I understand the equation correctly, it looks like they just factored 1/2 out. If you multiply, ie. 1/2 X 2h/g, you will get 2h/2g. Why didn't they just cancel the 2's out and end up with sqrt h/g? 🙂

 

[golgiapparatus88]

Thanks. I guess my question was why can't you just cancel out both the 2's and just have g/h? Is it cause g and h isn't the same variable? (sorry it's been a while)

 

[DavidMD2B]

Thanks. I guess my question was why can't you just cancel out both the 2's and just have g/h? Is it cause g and h isn't the same variable? (sorry it's been a while)

Sorry, I don't have that book but it looks like they factored the 1/2 out only to show that the variable you are looking for is 1/2 times 2h/g. If you figure out the meaning of 2h/g, you'll understand the purpose of the conversion.

 

[Kittee]

It's the one divided by half problem, which is equivalent to one times two.
In other words, 1 / (1/2) = 1 * 2 ==> 2

For the non-earth planet, they are saying t = sqrt[h / (1/2g)], which becomes t = sqrt[2h/g]

For the earth planet, you are correct in thinking t = sqrt[h/g]

In order to illustrate or compare the two, however, they are multiplying numerator and denominator by 2, and then just rewriting it to show a comparison:

t(of non-earth) = sqrt[2h/g] vs t(of earth) = sqrt[1/2 * 2h/g]
In other words, the time on earth is 1/1.4 that of the other planet.

The equation they are using is x = 1/2at^2 --> h = 1/2gt^2
(Ugh, I know it looks ugly. Does SDN have LaTex?) Maybe they made it more complicated and it might help to look at it in this form to get a better grasp.

I hope that helps. And yes, of course you can cancel out the 2's! But in their complicated opinion, I guess, it makes the relationship between the two planets harder to discern.