TBR Physics, Section 1, Passage 1, Question 2

[Abdominis]

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Can someone please explain the math in this question? It's confusing me.

 

[PiBond]

Can someone please explain the math in this question? It's confusing me.

new or old version? there's different passages in each

 

[Abdominis]

The copyright date on mine is 2008.

 

[PiBond]

The copyright date on mine is 2008.

Ok, I'm assuming you have the older version. Is it the question about Galileo and flight times?

 

[Abdominis]

Yes, that's the one. How do they get from (I'm trying my best to copy the notation here):

t(earth) = square root of 2h/2g(halfnia)

to

square root of 1/2 * (2h/halfnia)??

I just don't understand the math there. Maybe it's square roots that are confusing me.

 

[PiBond]

Yes, that's the one. How do they get from (I'm trying my best to copy the notation here):

t(earth) = square root of 2h/2g(halfnia)

to

square root of 1/2 * (2h/halfnia)??

I just don't understand the math there. Maybe it's square roots that are confusing me.

Ok, halfnia is just a theoretical planet with half the gravitational acceleration of earth (has 4.9m/s2 instead of 9.8m/s2). Therefore, we know that object A (which is on earth) will be accelerating to the ground faster than it would on hafnia. Therefore its flight time will be less--go ahead an eliminate A and D. Because there's different gravitational forces and we know that kinematics are involved we can go ahead and eliminate the answer choice that says that each object will have the same flight time. This would lead us to the correct answer B without even having to do math.

Here's the math part:
Since both objects are tossed from the top of the same rocket they have the same delta y's. All that's different is the gravitational acceleration. We can use the kinematic equation delta👍=vot + 1/2at^2. We know that both objects have zero initial velocity in the y-direction so we're left with this modified equation: delta👍=1/2at^2
Stone A (on earth): 20=1/2(9.8)t^2
Stone C (on halfnia): 20=1/2(4.9)t^2
The only thing that different numerically is the acceleration due to gravity (which is 1/2 on halfnia). Since we're finding time and need to take the square root, it ends up being 1/square root 2...answer B.

Hope that helps.

 

[Abdominis]

I understand everything in your explanation except that last part that begins with:

The only thing that's different numerically...

How do you arrive at the answer of 1/square root 2?

 

[Abdominis]

I mean, how do you arrive there mathematically?

 

[PiBond]

I mean, how do you arrive there mathematically?

The equations for flight time of Stone A and Stone C only differ numerically in their number for acceleration due to gravity. Stone A is tossed on earth so it accelerates to the ground at 9.8m/s2 and Stone C is tossed on halfnia so it accelerates to the ground at 4.9m/s2 (aka half of earth). If we solve for the time of each projectile on their respective planets we get:
Stone A: (20*2)/9.8 = t^2
Stone C: (20*2)/4.9 = t^2

We can leave out the numbers that are the same in both equations and focus on just the acceleration due to gravity for the sake of comparing their flight times.

1/9.8=t^2
1/4.9=t^2
Take the square root to find time and voila

Does that make sense?

 

[Abdominis]

Okay, now I get it. Thanks! You're a great help! I'm assuming you used TBR for the MCAT?

 

[helix]

what about the different Vo of the 2 drops?

 

[BerkReviewTeach]

what about the different Vo of the 2 drops?

If I remember the question correctly, aren't the two objects launched horizontally, which would mean that voy would be zero for both of them? That allows us to ignore the y-direction velocity when determining the drop/flight time.

 

[helix]

If I remember the question correctly, aren't the two objects launched horizontally, which would mean that voy would be zero for both of them? That allows us to ignore the y-direction velocity when determining the drop/flight time.

Yes, it was horizontal launch. Thank you!