Max height reached by projectile

[OneManShow]

This is from EK phys 1001 #86:
Which of the following represents the max height reached by the projectile?
The answer is h = 1/8gt^2
The way they founded was by setting t = 1/2 (since half the time will get you to max height) and initial velocity = 0
From x=vit +1/2at^2 they get h = 1/2(g)(1/2)^2
The math makes sense but one of the other answers is h = v^2/2g (which I thought was the answer)
from vf^2 = vi^2 + 2ax , if vf is zero at maximum height, then -vi^2 = -2gx
and x = height = vi^2/2g

but this is not the answer... can someone explain why?

---

Members don't see this ad.

 

[Pisiform]

May be because you messed up the sign: from vf^2 = vi^2 + 2ax , if vf is zero at maximum height, then vi^2 = -2gx
and x = height = -vi^2/2g

and the answer choice is positive which is why it is wrong.

 

[OneManShow]

May be because you messed up the sign: from vf^2 = vi^2 + 2ax , if vf is zero at maximum height, then vi^2 = -2gx
and x = height = -vi^2/g

and the answer choice is positive which is why it is wrong.

if vf is zero:
0 = vi^2 + 2ax
0 = vi^2 - 2gx
-vi^2 = - 2gx
vi^2 = 2gx

there's a negative in front of vi^2 b/c you are subtracting it from zero
I'm sure height = vi^2/2g
I just don't know why they chose the other one as the answer

 

[Pisiform]

if vf is zero:
0 = vi^2 + 2ax
0 = vi^2 - 2gx
-vi^2 = - 2gx
vi^2 = 2gx

there's a negative in front of vi^2 b/c you are subtracting it from zero
I'm sure height = vi^2/2g
I just don't know why they chose the other one as the answer

Haha I just read the question in the book.

v is the starting resultant velocity (of both components) while in the formula we will plug in 0 = (vSintheta)^2 + 2ax

 

[OneManShow]

Haha I just read the question in the book.

v is the starting resultant velocity (of both components) while in the formula we will plug in 0 = (vSintheta)^2 + 2ax

o ok I just realized that it was the resultant velocity. This is still a bad question though 🙁

 

[MT Headed]

o ok I just realized that it was the resultant velocity. This is still a bad question though 🙁

The AAMC practice tests have questions like this too, especially in the PS section. They are trying to separate those who blindly plug in formulas from those who deeply understand what is going on.

If this little gem teaches you to be a little more paranoid about the wording of questions in the future and not just jump to a distractor that looks good at first, consider it a well written question.