Abasketball is thrown straight up into the air and takes 2.5 seconds to reach the top of it's arc. the acceleration due to gravity is 9.8m/s ^2 downwards. what was the initial velocity of the ball?

Let say the basket ball is tossed upwards with initial speed "v"

now when it moves up in the air its speed will decrease due to acceleration of gravity in opposite direction

So here we can say that its final speed at the top position will be zero

here it will take t = 2.5 s to reach the top

now we can use equation of kinematics

now we have

so the ball is tossed up initially with speed 24.5 m/s

explanation:

newton's third law, for every action there is an equal and opposite reaction.