v(y)=v with letter y below normal line.

"Explain why you can use the formula v(y)=g(t/2) to calculate the initial vertical velocity."

My teacher claimed he explained the answer to this, but I didn't catch it. I would appreciate any help I get. THANKS!!! <3

All I can guess is that this is a object starting from rest, ending at time t. You want to know the average velocity during that time, which is equal to 1/2 the final velocity

avg velocity= (vf +Vi)/2
= (Vf+0)/2 = 1/2 g t