see da, the 'case' does not matter for taking sign convention.

 

these r the steps to solve sums correctly using sign conventions:

1) fix the +ve and the -ve directions

2) any vector (for eg, velocity vector, acceleration due to gravity vector) should be given the appropriate sign, depending on whether it is pointing towards the +ve or -ve directions, as fixed by you in step 1.

3) use newton's laws of motion equations, using the sign convention obtained for each vector in step 2 and SOLVE.

 

NOW, IN THE QUESTION ASKED BY U, LETS TAKE CASE 2:

following the steps ive given above,

1) lets say up is -ve & down is +ve (u can take it the other way round also...ok)

2) so now, g is +ve & v is -ve (say that v & g are of magnitude 10)

3) so if you want to find the max height it rises to for example, then

v² = u² + 2gH

0 = (-10)² + 2(10)H

20H = -100

so, H = -5 metres

 

see, now, just bcoz u r gettin the height as -ve, the answer is NOT wrong:

the reason for this is, u have taken up as -ve & down as positive, keeping the ground as origin, so all the displacements above the ground has to be -ve by this convention.

 

HOPE I HAVE MADE MYSELF CLEAR and the concept on conventions is clear...

PLS  << RATE >>  MY EFFORT.......