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ASTB prep test
- Thread starter Zeo
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The area of the given rectangle is 10 units. We know that one side is 5 units long, so given that the length times the width is the area of a triangle, the other side must be 2 units long.
Now that we know that, we know that the base of the given triangle is 2 units, and the height is 5 units, because point E is the same height as line AB, which is 5 units from D.
Following the formula for the area of a triangle; area = 1/2 base * height, we get 2(.5)* 5= area.
Thus, the area is 5 units.
Now that we know that, we know that the base of the given triangle is 2 units, and the height is 5 units, because point E is the same height as line AB, which is 5 units from D.
Following the formula for the area of a triangle; area = 1/2 base * height, we get 2(.5)* 5= area.
Thus, the area is 5 units.
No problem. It took me a minute when I saw it, too, I just wasn't looking at it right.
Good luck,
Neal
Good luck,
Neal
cherokeexj94
Registered User
I have 2 questions; #33 in the mechanical section, why would it take more force to raise the weight on pully 'A'? One would think that since both 'A' and 'B' have a mechanical advantage of 1, that they would be equal. My second question is what is the verbal section like on the ATSB, there is no mention of it in the gouges on this site and everyone also says that it is not like the verbal in the arco book.
cherokeexj94
Registered User
Hmmm, could i get a little more insight as to the reasoning for #33, i read the explaination on Mech advantage on the gouge attachments as well as search online about it, i found alot of stuff but nothing that clairifies this question for me. -thanks
SORRY... I WAS LOOKING AT THE WRONG SECTION.
I was wondering why it didn't make sense... I'll leave it posted in case someone wants the info.
(this is #33 from the math section)
Each aircraft is traveling at the same rate. At any given time, they will be equal distances away from the starting point.
If you create a triangle with the distance traveled by each aircraft as legs, it will be an isosceles triangle. By definition of an isosceles triangle, the angles at the base of each of those legs are equal.
If you add all the angles together, you get 180 for a triangle. With the angle of divergence between the two aircraft 60, you subtract that from 180 to get the value of BOTH bottom. Because they are equal, you divide by 2 to figure out what they are.
180 - 60 = 120. Divide by 2, and you have 60 for each angle.
Now you know the triangle is not only isoscles, but equilateral (all angles are the same). This also means all sides are the same.
When the aircraft are 1200 mile apart, they are each also 1200 mile from the starting point.
divide distance by velocity to get time.
1200 mile / 500mph = 2-2/5 hours
I was wondering why it didn't make sense... I'll leave it posted in case someone wants the info.
(this is #33 from the math section)
Each aircraft is traveling at the same rate. At any given time, they will be equal distances away from the starting point.
If you create a triangle with the distance traveled by each aircraft as legs, it will be an isosceles triangle. By definition of an isosceles triangle, the angles at the base of each of those legs are equal.
If you add all the angles together, you get 180 for a triangle. With the angle of divergence between the two aircraft 60, you subtract that from 180 to get the value of BOTH bottom. Because they are equal, you divide by 2 to figure out what they are.
180 - 60 = 120. Divide by 2, and you have 60 for each angle.
Now you know the triangle is not only isoscles, but equilateral (all angles are the same). This also means all sides are the same.
When the aircraft are 1200 mile apart, they are each also 1200 mile from the starting point.
divide distance by velocity to get time.
1200 mile / 500mph = 2-2/5 hours
#33 mechanical section
Mechanical advantage is determined by counting the number of ropes starting at the first MOVABLE pulley. In A the pulley is fixed, so there is no advantage. In B the pulley is movable, so you start counting the ropes there, and it have a mechanical advantage of 2.
So pulley A will take twice as much force to pull.
(it has been a while since I studied this, so I may not be 100% correct in the numbers, but the issue is the difference in a fixed pulley vs. movable pulleys - the ARCO book or the Thompson/ARCO book has a good explanation on how to determine the mechanical advantage of a system - I can't remember which one, and I deleted the files I had)
Mechanical advantage is determined by counting the number of ropes starting at the first MOVABLE pulley. In A the pulley is fixed, so there is no advantage. In B the pulley is movable, so you start counting the ropes there, and it have a mechanical advantage of 2.
So pulley A will take twice as much force to pull.
(it has been a while since I studied this, so I may not be 100% correct in the numbers, but the issue is the difference in a fixed pulley vs. movable pulleys - the ARCO book or the Thompson/ARCO book has a good explanation on how to determine the mechanical advantage of a system - I can't remember which one, and I deleted the files I had)
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