Writing impulse in vector notation

[xxascendantxx]

Homework Statement

A baseball strikes a bat. It's moving at 40m/s to the left horizontally. When it hits the bat it leaves at 60m/s with an angle of 30 degrees to the horizontal. The mass of the ball is 0.25kg.

Homework Equations

P(momentum)=mv
Pf-Pi=ΔP
ΔP=J(impulse)

The Attempt at a Solution

Since we are speaking in vector terms I would assume that 60 should be negative. But anyways the question asks to write the net impulse in vector notation. It reads it as J=Jxi + Jyj. Since change in momentum(delta P) is equal to impulse; If I was trying to find the impulse in each direction like the question asks, how could I do it?

I was thinking I could do:

the impulse for the x-direction should be: (0.25)(-60cos30) - (0.25)(40cos0)
the impulse for the y-direction should be: (0.25)(-60sin30) - (0.25)(-60sin0)

I ended up with: J=-26i -7.5j

Is this correct?

Thank you very much!

 

[haruspex]

I will assume the 30 degrees is above horizontal.
It's not that the 60m/s should be read as -60 (which affects both horizontal and vertical), but that the 30 degrees should be read as 150 degrees in relation to the initial velocity. Note that this makes the vertical change positive, as it should be.

 

[Chestermiller]

If home plate is the origin, and the horizontal direction away from home plate is the positive x-direction, and the upward direction is the positive y-direction, then then

initial x momentum = -(0.25)(40)
initial y momentum = 0

final x-momentum = +(0.25)(60 cos(30))
final y-momentum = +(0.25)(60 sin(30))

Impulse of force = change in momentum = (final momentum) - (initial momentum)