Why does a rocket have such great momentum even if it is moving at a slow speed?

Momentum of an object is the product of two quantities:

Momentum = (the object's mass) times (the object's speed)

If one of these quantities is small, the momentum can still be large if the other quantity is huge.

A rifle bullet is a great example of this idea. The bullet has a small mass ... maybe only a few grams ... but it gets shot out of the rifle with such a high speed that when you multiply (mass) x (speed), the bullet has enough momentum to knock a big person down off his feet.

Rockets provide a wonderful example of Momentum Conservation. As momentum in one direction is given to the rocket's exhaust gases, momentum in the other direction is given to the rocket itself.

Explanation:

First, think of two masses connected by a lightweight (massless!) compressed spring. When the two spring apart, conservation of momentum tells us the Center of Mass remains where it was (or moving as it was).

PTot, i = p1i + p2i = 0 + 0 = 0

PTot, f = p1f + p2f = PTot, i = 0

p1f + p2f = - m1 v1f + m2 v2f = 0