Solve Direction of Impulse: Linear Momentum & Force

[jtmbii]

This should be a quick question. I'm not understanding the overall concept of impulse/force direction very well. I appreciate your help.

Homework Statement

The 0.5kg ball strikes the rough ground and rebounds wit the velocities as shown. Determine the magnitude of the impulse the grounds exerts on the ball in the x direction. Assume that the ball does not slip when it strikes the ground, ,and neglect the size of the ball and the impulse produced by the weight of the ball.

Homework Equations

Principle of Linear Impulse and Momentum:

The Attempt at a Solution

I started off with the following

then got F = -4.509 N
I then realized that impulse should be in the negative direction(?) Thus, to get a positive value of force like the answer in the book, the equation should be:

Is this correct? But I cannot understand why. Time is scalar so impulse direction should depend on the direction of the force (?) Though how am I supposed to tell this direction? To me, it looks like the force is positive in the x direction before it hits the ground, and after. This is why I am confused. I want to understand this more visually. Thank you.

 

[Doc Al]

Is this correct? But I cannot understand why. Time is scalar so impulse direction should depend on the direction of the force (?) Though how am I supposed to tell this direction? To me, it looks like the force is positive in the x direction before it hits the ground, and after. This is why I am confused. I want to understand this more visually. Thank you.

You were right the first time. The impulse is negative (the momentum decreases), meaning the force is opposite to the direction you took as positive. No big deal. All you care about is the magnitude anyway.

 

[jtmbii]

You were right the first time. The impulse is negative (the momentum decreases), meaning the force is opposite to the direction you took as positive. No big deal. All you care about is the magnitude anyway.

Momentum decreases. I see. Thank you so much for this.