The initial velocity of a ball sent upward from the ground, is 12 m/s. What will its final velocity be before it hits the ground O 12 m/s
0-12 m/s
0 -9.8 m/s
O 9.8 m/s

The final velocity s 12 m/s.

For the upwards trajectory:   (using the positive value of g in the downward direction)

Vf = Vi - g t = 0   where Vi is initial velocity and Vf the velocity at max height

Vf = 12 - g t = 0      t = 12 / g     time to reach max height

For the downwards trajectory

Vf = Vi + g t = 0 + g t    =  g * 12 / g = 12  where t was found above

We know the from  2 g h = Vf^2 - Vi^2, since the height is the same in both directions, that the ball reaches the ground with at the same speed at which it was sent.

Also, conservation of energy shows that the ball must return to the ground with the speed with which was projected.

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