# Direction of impulse

How do we know the direction of the impulse(which is the change in momentum)? I thought lets say if an object travels at -ve x direction at a certain speed and someone hits it back at another speed (towards the +ve x direction), how do we tell the direction of the impulse? Isnt the direction always in the +ve direction in this case if we have defined our +ve and -ve directions as stated???So its always true that the impulse is in the final direction?

Cos final momentum - initial momentum = change in momentum =impulse. So it will always be in the direction of the final velocity right?

## Answers and Replies

Yup, you are correct.

thanx alot!

andrevdh
Homework Helper
That is only true if the impulse force succeeds in changing the direction of the motion of the object (if it acts against it to start with) - think of a bug hitting the windscreen of a truck, it will slow the truck down by a bit only momentarily without changing the direction of it's motion.

HallsofIvy
Science Advisor
Homework Helper
Nope, you are completely wrong!

Your statement "the impulse is in the final direction?" is, in general, false!

IF you are dealing with motion on a straight line and IF the impulse is enough to reverse the direction of motion then, yes, the impulse happens to be in the same direction as the final motion. However, in one dimension there are only two possible directions so there aren't that many possiblities!
Suppose you have an object moving along a line and you give it "hit" that slows it down to 1/2 its speed. In that case, the "final speed" is still in the same direction and opposite to the impulse. There are only two possible directions (same or opposite final speed) and impulse can take either!

If you work in two or three directions, it's much more complicated. Imagine a pool ball bouncing off a cushion. The impulse is perpendicular to the cushion but neither the initial nor final speeds are in that direction.

The best thing to say is "impulse is change in momentum: subtract the two momenta." Since momentum is mass*velocity and mass has no direction, as far as the direction is concerned, subtract the initial velocity from the final velocity.

In the example you gave: inital velocity -ve, final velocity +ve, ve-(-ve)= +2ve. The impulse is in the + direction, the same as the final velocity. In the example I gave, initial velocity is ve, final velocity is (1/2)ve, impulse is (1/2)ve- ve= (-1/2)ve, opposite to the final velocity.

For the pool table example, take initial velocity vector to be (vx, -vy), final velocity (vx,+vy). The impulse is the difference of those vectors: (vx, vy)- (vx,-vy)= (vx-vx, vy+vy)= (0, vy), not in the direction of either initial or final velocity.

Oh! Thanx for the explanation! I really UNDERSTAND now from your examples given! Appreciated! :)