Which object would have the most momentum?

a. a 500-pound car moving at 20 miles per hour

b. a 200-pound car moving at 60 miles per hour

c. a 100-pound car moving at 80 miles per hour

d. a 50-pound car moving at 100 miles per hour

Momentum is directly proportional to mass and speed.

When working with SI units, the interoperability of the units

is all taken care of. The proportionality constant is ' 1 ', and

we can simply say

Momentum = (mass, in kg) x (speed, in m/s).

In other systems of units, such as the ponderous and complex

'customary' one referenced in this question, the proportionality

constant isn't ' 1 ', but momentum is still directly proportional

to mass and speed. So if all we need to find is the greatest

momentum from a list, we can simply look for the greatest

product and not worry about the units. The actual numbers

won't mean much, but each product is still directly proportional

to the mass and speed that are its factors, so the greatest

momentum can easily be identified.

a). 500 x 20 = 10,000 'pound-mph'

b). 200 x 60 = 12,000

c). 100 x 80 = 8,000

d). 50 x 100 = 5,000

(b). has the greatest product, and therefore the greatest momentum.

For a meaningful number, we'd still need to do some work on the units.