In an automotive engineering lab, students are testing collisions between toy mo

Question

In an automotive engineering lab, students are testing collisions between toy models of cars. In one experiment, car A has a mass of 18.3 kg and an initial velocity of 10.39 m/s, traveling due east. Car B has a mass of 31.2 kg and an initial velocity of 7.48 m/s, traveling due north. They collide and stick together in a completely inelastic collision in which momentum is conserved. Find the magnitude and direction (relative to due east) of the total momentum of the two-object system after the collision. Enter the answers in the space provided, using the following example format: 50.32 N, 36.4 degrees.

Explanation / Answer

The conservation of the East momentum

mv = (M +m)v

(18.3)(10.39) = (18.3 + 31.2)(v)

v east = 3.84 m/s

The conservation of the North momentum

(31.2)(7.48) = (18.3 + 31.2)(v)

v = 4.71 m/s

The net velocity is from the pythagorean theorem

net2 = (4.71)2 + (3.84)2

net = 6.08 m/s

The angle is from the tangent function

tan(angle) = 4.71/3.84

angle = 50.8o

In summary, that is 6.08 m/s at 50.8o above due east

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