Question

If a 1000kg car is moving to the East at 12m/s and collides into a 3000kg car moving North at 2m/s, what is the momentum and velocity of the wreckage?

Answer 1

You have two things to figure out here and they are both vectors

momentum = mass * velocity
east car momentum = 1000 kg * 12 m/s = 12,000 kg m/s
north car momentum = 3000 kg * 2 m/s = 6,000 kg m/s

So make a right triangle of 12000 on bottom and 6000 on vertical and figure out hypotenuse, you can cancel out zeroes to make easier

a^2 + b^2 = C^2
12^2 + 6 ^2 = C^2
144+36 =C^2
c = sq rt [ 180]
c = 13.4 (adding back the zeroes), = 13,400 kg m/s momentum
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Velocity vector is a right triangle also:
a^2 + b^2 = C^2
(12 m/s)^2 + ( 2 m/s)^2 = c^2
c = sq rt [ 144 + 4]
c = 12.2 m/s velocity
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