how do i slove this question?

Question

Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v= square root 19.6h If an object hits the ground with a velocity of 15.5 meters per second, from what height was it dropped?

Answer 1

h(t) = -16t² -vt + h(0)

height equals the initial height minus 16t² which reflects the acceleration of gravity and minus v is the initial velocity. but here apparently initial v=0

it hits the ground at v=15.5, where the final velocity is all due to the acceleration from gravity

0=-9.8t² - vt + h(0) = -9.8t² + 0 + h(0) = 0

velocity is the derivative of acceleration or -19.6t = -15.5 when it hits ground, so

solve for t, t=15.5/19.6 or less than a second

h(0) = 9.8t = 9.8(15.5/19.6) = 15.5/2 = 7.75 meters high = initial height

I'm not sure what the v= square root 19.6h means. It doesn't fit the standard equation for objects falling due to gravity. 19.6 is the coefficent of time t, when you take the first derivative of 9.8t² and that first derivative is velocity