Calculating Impulse in a Baseball Pitch and Hit

[hbomb]

A baseball pitcher delivers a fastball that crosses the plate with an angle of 5.67 degrees relative to the horizontal and a speed of 80.1 miles/hour. The ball (mass 0.145 kg) is hit back over the head of the pitcher at an angle of 37.09 degrees with respect to the horizontal and a speed of 108.5 miles/hour. What is the magnitude of the impulse received by the bat?

Ok, impulse is the change in momentum.
p=m(vf-vi)
But since the mass is pitched at an angle and is hit at an angle you need to decompose the velocity vector into it's y and x components.

vyi=(35.81)sin(180-5.67)=3.54 m/s
vxi=(35.81)cos(180-5.67)=-35.63 m/s

vyf=(48.50)sin(37.09)=29.25 m/s
vxf=(48.50)cos(37.09)=6.78 m/s

Add the x and y components to each other
y's=25.71 m/s
x's=42.41 m/s

Then find the velocity of the summed vectors
vf=sqr(vx^2+vy^2)=49.6 m/s

p=mv=(0.145 kg)(49.6 m/s)=7.192 kg m/s

When I enter this into my homework site for my class, it tells me this is the wrong answer. I'm I missing something here? At first I thought maybe I'm not suppose to find the difference between 180 and my angles for the intial velocties. So I tried it just with the original angles and I still get a wrong answer message. Please help.

http://img138.imageshack.us/img138/2597/baseballyg4.jpg

 

[Fermat]

Hmm, I know very little about baseball (I'm a brit) but when that fastball is crossing the plate, is that the pitcher's plate,or the home plate ??

 

[hbomb]

Home plate

 

[Fermat]

vxf=(48.50)cos(37.09)=6.78 m/s

that should be 38.69

Add the x and y components to each other
y's=25.71 m/s
...

you subtracted instead of adding here.

 

[hbomb]

What is the correct anwer, because I fixed the mistakes and I'm still getting a wrong answer message. Right now I have 29.25+3.54 for the y's because the vectors are going in the same direction. For the x's I have 38.69-35.63 because the vectors are going in opposite directions. I get 4.77 kg m/s for the impulse. Is this right?

 

[Fermat]

You've been subtracting the x's instead of adding them.
Before impact, the ball has a speed of 35.63 m/s to the right (going by your diagram)
After impact, the ball has a speed of 38.69 m/s to the left (going by your diagram)
So the overall change in velocity (which is a vector) is the sum of the speeds = 74.32 m/s.

Edit: I get 11.78 kg m/s as the change in momemtum.