What equation to use for projectile motion problems

[pickle37]

I was given a list of equations for projectile motion and two of the equations have the same variables but give different outputs. I don't understand when to use one equation and when to use the other. The equations are:

ay=(vfy-viy)/(delta t)

and

(vfy)^2= (viy)^2 + 2ay(delta t)

I tried using the second equation to solve the following problem but got it wrong. In the book they used the first equation. I see how using the first equation makes sense now, but why is it wrong to use the second equation?

A marble rolls off a table at the horizontal velocity of 1.93 m/s. The tabletop is 76.5 cm above the floor. If air resistance is negligible, determine the velocity at impact.

I solved for (delta t) and got 0.4s. I rearranged the second equation to find (vfy) and tried to solve using (viy)=0m/s, ay= 9.8 m/s^2, and (delta t)= 0.4s . I found (vfy) to be 2.8 m/s when its supposed to be 3.9 m/s

 

[jorrty]

Recheck your second equation. Are you sure 'delta t' isn't 'delta y'?

 

[pickle37]

They have (delta t) written in the textbook

 

[jorrty]

Everything looks good except I think your second equation isn't quite right. 0.4s is correct. What textbook is this?

 

[jtbell]

The second equation should definitely have $\Delta y$ instead of $\Delta t$. If your book has $\Delta y$ there, it's a misprint.