Momentum as a Vector

Momentum is defined asp = mvwhere m is the mass (kg) and v is the velocity (m s^-1). Its unit is kg m s^-1, which is the same as N s. Because velocity is a vector, momentum is a vector: it has both magnitude and direction, and points in the same direction as the velocity.In one dimension, direction is shown by a sign: choose one direction as positive, and momentum in the opposite direction is negative. In two dimensions, momentum is drawn as an arrow and can be resolved into perpendicular components, just like any vector:p_x = p cosθ     p_y = p sinθwhere θ is the angle between the momentum and the x-direction. Momenta are combined by vector addition (tip to tail, or by adding components), never by simply adding magnitudes.Worked example 1: a 0.50 kg ball moves at 12 m s^-1 at 30° above the horizontal.
p = 0.50 × 12 = 6.0 kg m s^-1
horizontal component = 6.0 cos 30° = 5.2 kg m s^-1
vertical component = 6.0 sin 30° = 3.0 kg m s^-1Worked example 2: a 0.20 kg ball hits a wall at 5.0 m s^-1 and rebounds at 5.0 m s^-1. Taking the rebound direction as positive:
Δp = (0.20 × 5.0) – (0.20 × –5.0) = 2.0 kg m s^-1
The change is not zero: the speed is the same, but the direction has reversed.