4. A dump truck has a mass of 5.50 x 105 kg when loaded and 2.30 x 105 kg when empty. Suppose two such trucks, one loaded and one empty, crash into each other
at a monster truck show. The trucks are supplied with special bumpers that make
a collision almost perfectly elastic. If the trucks hit each other at equal speeds of
5.00 m/s and the empty truck recoils to the right with a speed of 9.10 m/s, what is
the velocity of the full truck after the collision?

V = 0.896 m/s

Explanation:

This is a typical problem of momentum conservation, whic states the following:

m₁V₁ + m₂V₂ = m₁V₃ + m₂V₄   (1)

In this case V₃ and V₄ would be the final velocity of the trucks after the collision.

With the given data let's see what we have:

m₁ = 5.5x10⁵ kg

m₂ = 2.3x10⁵ kg

V₁ = 5 m/s

V₂ = -5 m/s because it's going to the left (-x axis)

V₄ = 9.1 m/s to the right (Meaning is positive)

V₃ = ??

So to calculate V₃ we just need to replace the data into (1) and solve for V₃:

(5.5x10⁵ * 5) - (2.3x10⁵ * 5) = 5.5x10⁵V₃ + (2.3x10⁵ * 9.1)

2.75x10⁶ + 1.15x10⁶ = 5.5x10⁵V₃ + 2.093x10⁶

V₃ = 2.75x10⁶ - 1.15x10⁶ - 2.093x10⁶ / 5.5x10⁵

V₃ = -0.493x10⁶ / 5.5x10⁵

V₃ = -0.896 m/s

With this sign, it means that is going in the same sense of the other truck, but it's going to the left so this would be positive:

Hope this helps

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