Baseball in the air 2D motion question

[Kyros]

Homework Statement

A baseball is hit into the air, nearly vertically, with a speed of 27 m/s. When it comes down, the ballplayer catches it in his glove. Air resistance (drag) is actually fairly important for a baseball in flight, but for now let’s assume it is negligible.

(a) How high does the baseball go, and how long is it in the air?

(b) As the player catches the ball, his glove moves downward by 12 cm before coming to rest. Based on this, estimate the acceleration of the ball as it is caught.

Variables:
V=27 m/s
Acceleration= g= 9.8
Vo= 0 m/s
Xo=0 m
x=?
t=?

Homework Equations

kinematic equations for constant acceleration:
V=Vo+at
X=X0+V0t+1/2at^2
V^2=Vo^2+2a(X-Xo)
Average V= (V+Vo)/2

v= change in x/ change in t
a= change in v/change in t

The Attempt at a Solution

[/B]
a.
V= Vo+(at)
27= (0)+ 9.8t
t= 2.76 seconds

X=Xo+Vot+1/2at^2
x=(0)+(0)(2.76)+1/2(9.8)(2.76)^2
x=37.32m

b.
this is where i get lost...
12cm= .12m

x= 37.32 +.12m = 37.44m
t= 2.76 seconds

v= 37.44 /2.76 = 13.57m/s

a= 13.57m/s/2.76
a= 4.92Thats my attempt, I'm really lost so any advice or help will be appreciated. I'm not too confident about my answer but a too. Also, is b just 9.8? since its just gravity acting on the ball.

 

[haruspex]

the acceleration of the ball as it is caught.

Not sure if you understood this. It is asking for the acceleration from the moment the ball touches the gloves until it comes to rest.

x= 37.32 +.12m = 37.44m

Adding the two distances is not useful. The kinetics equations you use ("SUVAT") only apply while the acceleration is constant. When the gloves make contact, the acceleration changes.
Treat the process of catching as entirely separate.

There is a small flaw in the statement of the question. It ought to tell you to assume this catching acceleration is constant.