Please help solve, attempted answer is listed from another chegg user but was in

Question

Please help solve, attempted answer is listed from another chegg user but was incorrect.
Free Fall | You are situated at the top of a building of height, h. Your friend is poised to drop a ball from a window at height above the ground. Find an expression for the speed at which you should simultaneously throw a ball downward so that the two balls hit the ground at the same time. Neglect air resistance. Your expression should be in terms of the given variable and any other known constants such as acceleration due to gravity, g h gt Incorrect. Tries 4/6 Previous Tries

Explanation / Answer

time taken by both the balls to reach ground should be same.

for the ball dropped from height of h/2:

initial speed=0

distance=h/2

acceleration=g

then using the formula;

distance=initial speed*time+0.5*acceleration*time^2

==>h/2=0*t+0.5*g*t^2

==>t=sqrt(h/g)..(1)

for the ball thrown from height h:

let initial speed=u

distance=h

acceleration=g

then using the formula;

distance=initial speed*time+0.5*acceleration*time^2

==>h=u*t+0.5*g*t^2

from equation 1, t=sqrt(h/g)

==>h=u*sqrt(h/g)+0.5*g*(h/g)

==>h=u*sqrt(h/g)+0.5*h

==>h/2=u*sqrt(h/g)

==>u=0.5*h*sqrt(g/h)=0.5*sqrt(g*h)

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