At a busy intersection a 1540-kg car traveling west with a speed of 12 m / s collides head-on w

step 1 Here in this question we are going to calculate the mass of the van So here we consider that the

At a busy intersection a 1540-kg car traveling west with a...

At a busy intersection a $1540-\mathrm{kg}$ car traveling west with a speed of $12 \mathrm{~m} / \mathrm{s}$ collides head-on with a minivan traveling east with a speed of $9.4 \mathrm{~m} / \mathrm{s}$. The cars stick together and move with an initial velocity of $1.5 \mathrm{~m} / \mathrm{s}$ to the east after the collision. What is the mass of the minivan?

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Key Concepts

Inelastic Collision

An inelastic collision is one in which the colliding objects stick together after impact, moving as a single combined mass. In these collisions, while momentum is conserved, kinetic energy is not necessarily conserved, making the conservation of momentum the primary tool for problem-solving.

Vector Direction and Sign Conventions

When dealing with momentum and collisions, assigning a positive and negative direction is crucial to account for the vector nature of velocity. Establishing a consistent sign convention allows for accurate application of the conservation laws to determine unknown quantities, such as mass or velocity.

Conservation of Momentum

This concept states that in the absence of external forces, the total momentum of a system remains constant before and after a collision. It is a fundamental principle used to analyze collision problems by equating the sum of momenta of all objects before the collision with the sum after the collision.

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