What the difference between these two formulas?

Question

D=vi(sinΘ)(t)+1/2(g)(t)²

^and

dy=vf² - vi²/ 2g

I thought that both of them solve for the maximum height or "peak" of a projectile however when I used them in problems I received diffrent answers.

I have no idea what each of them is used for.

Answer 1

The first is just a kinematic equation in the 'y' direction. Yes, this is for height (D).

The second is also a kinematic equation (that needs a slight adjustment) for change in position ('height' if in the 'y' direction).

My guess is that order of operations got messed up in the second formula because of how it is written.

The second equation should be written:

dy = (v_f² - v_i²)/(2g)

and be careful with the order of operations!