3 different equations for finding final velocity in y direction..which is right?

Question

v_y = v_y_0 + a*t

y= y_0 + v_y_0 * t +1/2*a*t^2

v_y^2 = v_y_0^2 + 2*a*(y-y_0)

I know that v_y_0 = 0 and y_0 = 0 (a ball is rolling off a ramp and I need to figure out the final velocity in the y direction) I know the values of y, a (9.8), and time. Each equation I use, however, produces different results. What am I doing wrong here?

Answer 1

Your equations are dissimilar. Double check them. Then try your values again. Also, given the initial values, all three equations might not be correct. The first equation is suspect. The third equation is suspect. Double check them.

Answer 2

Your first equation is simply the derivation of the second one, as the velocity is the derivate of the position (v = x', a = x'' = v'). So both are correct. The third one is the same as the second one but expressed differrently.
Maybe are you confusing v_0 and v_y0 (v_0 is the (v_x0,v_y0) vector).
If you want to resolve this type of problem you must make a clear schema and represent the forces, the initial velocities, etc... And use the Newton's law : F= ma (I can't put the arrows but this is a vectorial equation (x,y,z), F = m*dv/dt, F = m*d2x/dt. Apply it to all axes.
But in this case, and for the y axis, your equations are all correct and should give strictly the same result.

Answer 3

All these equations should produce the same result. I don't know what the previous poster is talking about. All three equations are accurate kinematics equations depending on how you are using them. Which way have you defined as the positive y-direction? This may be why your answers are not coming out correct.