You know .
Let U be the speed of the ball after being struck by the bat. Then the vertical and horizontal components of are and respectively.
Making the usual assumptions (negligible air reistance, no crazy spin on ball etc.) you can apply the straight line motion formula for constant acceleration in the vertical and horizontal directions of the balls motion:
Horizontal direction: x = 180 ft, , a = 0, t = ?
Substitute the data into to get equation (1).
Vertical direction: x = 0, , a = -32 ft/sec^2, t = ?
Substitute the data into to get equation (2).
Solve equations (1) and (2) simultaneously for U. Use this value to get the components of and hence . I'm too lazy to check if the value of U agrees with your value .....
So now you can write down the impulse.