Where does the -2 come from in Δp_x = -2mv cos(θ)?

[tanmandu]

Trying to Understand Where this Constant Came From in the "X component of Momentum"

After asking for help on this problem, my professor showed me how to derive the formula needed to solve the following question. However, it sliped my mine to ask where the "-2" came from.

Homework Statement

A 7kg steel ball strikes a wall with a speed of 8.74m/s at a angle of 37.3 degrees with the normal of the wall. It bounces off with the same speed and angle. If the ball is in contact with the wall for 0.301 seconds, what is the average force exerted on the ball by the wall?

Homework Equations

Change in Momentum in the X=-2MVcos()

The Attempt at a Solution

Using the formula, and knowing the is no change in the momentum in the Y direction I found the answer to be 323.369 N.

Like I said, what I am unclear about is where the -2 came from in the formula. Thanks.

 

[rock.freak667]

Change in momentum = Momentum after impact - Momentum before impact

Remember that momentum is a vector quantity, they took the x⁺ direction as positive.

Since the ball bounces back, it moves opposite to the initial direction (+), so the final momentum is negative

change in momentum = -a -a = -2a, it becomes like that.

 

[tanmandu]

Thank you so much. It is clear to me now.