Question

"The impulse given to a 2-kg object that goes from moving at 3 m/s in the + x-direction to 7 m/s in the + y-direction in 5 seconds is 8 kg m/s since the impulse equals the change in momentum. The 5 seconds does not enter into a calculation of this impulse." What, if anything is wrong with this description? If anything is wrong, identify it and explain how to correct it. Please include explanation for why the momentum needs to be squared rooted.

Answer 1

The 8 kg m/s is incorrect since the impulse and the change in momentum are vector quantities and this description does not treat them as such. Using a coordinate axis with positive x to the right and positive y toward the top of the page, the final momentum of the object is zero in the x-direction, so the change in momentum in the x-direction is –6 kg m/s. The initial momentum of the object in the y-direction is zero, so the change in momentum in the y-direction is 14 kg m/s. We can use the Pythagorean Theorem to find the magnitude of the change in momentum, which is 15.2 km/s. The direction of the change in momentum is 23.2 degrees to the left of the positive-y axis.