# A model truck A of mass 1.2 kg is travelling due west with a speed of 0.90 m/s . A second truck B of mass 4.0 kg is travelling due east towards A with a speed of 0.35 m/s .

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a)  Calculate the magnitude of the total momentum of the trucks.

The momentum (p) is the mass (m) of an object multiplied by its velocity (v).

p = m x v

Velocity is different to speed, because it has a direction. Fortunately, the trucks in the question are travelling in exactly opposite directions, so we can express their velocities, one compared to the other, as one being negative, and the other one being positive. Lets decide to make "travelling due east" positive, and "travelling due west" negative.

momentum of truck A = mass of truck A x velocity of truck A
p1 = m1 x v1 = 1.2 kg x - 0.90 m/s = - 1.08 kg.m/s

momentum of truck B = mass of truck B x velocity of truck B
p2 = m2 x v2 = 4.0 kg x 0.35 m/s = 1.4 kg.m/s

total momentum of the trucks = momentum of truck A + momentum of truck B
p(total) = p1 + p2 = - 1.08 kg.m/s + 1.4 kg.m/s = 0.32 kg.m/s

The total momentum is positive, which means that it is in the east direction, or in the direction of truck B.

If we look back at the numbers, we see that the mass of truck B is 3.3 times bigger than mass of truck A (4.0 / 1.2 = 3.3), while the speed of truck B is only 2.6 times smaller than the speed of truck A (9.0 / 0.35 = 2.6), so it makes sense that truck B has greater momentum.

b) The trucks collide and stick together. Determine their velocity after the collision.

The trucks stick together after collision. When this happens we can assume that they become one big truck. The mass of the new truck will be:

mass of big truck = mass of truck A + mass of truck B
m3 = m1 + m2 = 1.2 kg + 4.0 kg = 5.2 kg

We also assume that the trucks are in a closed system, meaning that the total momentum before the collision is the same as the total momentum after the collision. We can write this as:

p1 + p2 = p3

or

m1v1 + m2v2 = m3v3

The question asks us to determine the velocity after the collision. We can therefore rearrange the equation above to solve for v3.

v3 = (m1v1 + m2v2) / m3 = 0.32 kg.m/s / 5.2 kg = 0.06 m/s

After the collision, the two trucks will be travelling together due east at a speed of 0.06 m/s.

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