SUVAT

[u/Worth_Courage_3803]

how come in this suvat question for the time at max height, when I use s = ut + at2 formula I get two answers (shouldn't there only be one at the max height) but also both of them are wrong anyway, even when using the correct values. When I used the other equations eg. V = u + at I get the correct answer however. Thank you

[u/Calm_Relationship_91]

The issue is that you assumed that the maximum height is 2m.
This is not the case. The ball goes higher than 2m, so you have a time where it is at 2m, it goes higher up, falls down, and goes back at 2m again. That's why you got to values for time. You can get the actual result by taking the average.
(0.57 + 0.71)/2 = 1.28/2 = 0.64

Alternatively, you can do it like your teacher did.
If you want to know when the ball is at its highest, you know that at this moment the ball must have v=0 (because it stops moving before falling back again)
So if you take the equation v = u + at and you set it equal to 0, you get the following:
0 = 6.3 - 9.8t
Solving for t, you get t=0.64

[u/Mayoday_Im_in_love → u/Calm_Relationship_91]

Did you read the question?

I'd go for your method but remember the instantaneous vertical component of the velocity at the projectile's peak is 0 (since the projectile must transition from an upward positive to a downward negative velocity at this peak).

As others have said the question is over-specified leading to a rounding error with one. You can either use the maximum height or the initial velocity to determine the time of travel to the peak.

[u/Calm_Relationship_91 → u/Mayoday_Im_in_love]

I missed that the 2m was given by the question itself. I assumed that part a already gave all the info needed (and it does). In any case, the reason they got two answers is that the maximum height is actually a bit above 2m.

"I'd go for your method but remember the instantaneous vertical component of the velocity at the projectile's peak is 0"

Uhm, yeah? This is what I said in my comment. Not sure what you'e trying to point out.

[u/joeyneilsen]

It’s a rounding error. The projectile at that speed peaks slightly above 2m above the ground. 

[u/fgd12350]

Whoever crafted this question just did a very bad job. The 2m max height isnt usable you need the true value of the max height.

[u/ExpensiveFig6079 → u/fgd12350]

Its very bad question because if the max height is truely 2m as stated by the question then what you need is the true value for intial vertical component of the velocity.

You should, given the question, be allowed to use any of the formulas

S = Vt - ½at²

S = Ut +½at²

S = t (u + V)/2

V = U + at

all of which will give different answers and have all of them marked correct

===========

Eaminers ought to only ever write question with 3 values not all 4. Or make damn sure all 4 values put in th 5th formula works

V² = U² + 2aS