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A 1,103 kg car traveling at 18 m/s to the south collides with a 4,919 kg truck that is initially at rest at a stoplight. The car and the truck stick together and move together after the collision.

What is the final velocity of the two-vehicle mass? Round to the hundredths place.

Answer :

ANSWER

[tex]3.30\text{ m/s}[/tex]

EXPLANATION

Parameters given:

Mass of car, mc = 1103 kg

Mass of truck, mt = 4919 kg

Initial velocity of car, uc = 18 m/s

Inital velocity of truck = 0 m/s

To solve this problem, we have to apply the law of conservation of momentum, which states that the total momentum of a system is constant.

This implies that:

[tex]m_cu_c+m_tu_t=m_cv_c+m_tv_t[/tex]

Since the car and the truck stick together after the collision, they will have the same final velocity.

Hence:

[tex]m_cu_c+m_tu_t=(m_c+m_t)v_{}_{}[/tex]

Substitute the given values and solve for v (final velocity):

[tex]\begin{gathered} (1103\cdot18)+(4919\cdot0)=(1103+4919)v \\ \Rightarrow19854=6022v \\ \Rightarrow v=\frac{19854}{6022} \\ v=3.30\text{ m/s} \end{gathered}[/tex]

That is the final velocity of the two-vehicle mass.

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