BRAVO! You got it right!

Since we are not particularly interested in the time, we can use

v² = v_i^{2 + 2 a (x - x_i)}

one of our "Big Three Kinematics Equations" which will come in very, very handy as we study motion.

Remember, of course, that v is the "final velocity" or v is the velocity when the position is x. We are looking for the velocity at the top so that means v = 0 and x = x_{top. xi is the initial position; xi = 0.Gravity is the only thing affecting this motion; so this is a free fall problem. That means}

a = - g = - 9.8 m/s²

That minus sign is important!

Okay, we have all the pieces; let's put them together.

v² = v_i^{2 + 2 a (x - x_i)}

0 = (25 m/s)² + 2 ( - 9.8 m/s²)( x - 0 )

Do a quick check of units!,

0 = (25 m/s)² + 2 ( - 9.8 m/s²) x

2 ( 9.8 m/s² ) x = (25 m/s)²

x = ( 625/19.6) m

x = 31.9 m