Abaseball is hit so that it travels straight upward after being struck by the bat. a fan observes that it takes 2.90 seconds for the ball to reach its maximum height. a) find the balls initial velocity b) find the height it reaches

We'll assume that the whole scene takes place on Earth.
So the acceleration of gravity is 9.8 m/s² downward.

a).  Gravity makes anything fall 9.8 m/s faster every second.
That's the same thing as rising 9.8 m/s slower every second.

If it takes 2.9 seconds to reach its maximum height, then
it must have started out rising at (9.8 x 2.9) = 28.4 m/s.

b).  The ball left the bat at 28.4 m/s.
After 2.9 seconds, its speed was zero. (That's why it started falling.)
It's average speed during the climb was

                 1/2 (28.4 + 0)  =  14.2 m/s .

It rose straight up at an average speed of 14.2 m/s for 2.9 seconds,
so it reached a maximum  height of

                 (14.2 x 2.9)  =   41.2 meters    .