Two vehicles are approaching an intersection. One is a 2500-kg pickup traveling at 14.0 m/s from east to west (the -x-direction), and the other is a 1500-kg sedan going from south to north (the +y-direction) at 23.0 m/s. Find the x- and y-components of the net momentum of this system.

Verified step by step guidance

1. Step 1: Understand the concept of momentum. Momentum is a vector quantity defined as the product of an object's mass and velocity. The formula for momentum is given as $p=mv$, where $p$ is momentum, $m$ is mass, and $v$ is velocity.
2. Step 2: Calculate the x-component of momentum for the pickup truck. Since the pickup is traveling in the -x direction, its momentum will be negative. Use the formula $p$_x = mv_x, where $m$ is the mass of the pickup (2500 kg) and $v$_x is its velocity (-14.0 m/s).
3. Step 3: Calculate the y-component of momentum for the sedan. Since the sedan is traveling in the +y direction, its momentum will be positive. Use the formula $p$_y = mv_y, where $m$ is the mass of the sedan (1500 kg) and $v$_y is its velocity (23.0 m/s).
4. Step 4: Add the x-components of momentum to find the net x-component of momentum. Since only the pickup contributes to the x-direction, the net x-component is simply the pickup's momentum in the x-direction.
5. Step 5: Add the y-components of momentum to find the net y-component of momentum. Since only the sedan contributes to the y-direction, the net y-component is simply the sedan's momentum in the y-direction.

Key Concepts

Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity. It is expressed as p = mv, where p is momentum, m is mass, and v is velocity. In a system of multiple objects, the total momentum is the vector sum of the individual momenta, which is crucial for analyzing collisions and interactions.

Vector Components

Vector components are the projections of a vector along the axes of a coordinate system, typically the x and y axes in two-dimensional space. For momentum, this means breaking down the total momentum into its x-component (horizontal) and y-component (vertical). This decomposition allows for easier calculations and understanding of the system's behavior in each direction.

Conservation of Momentum

The conservation of momentum principle states that in a closed system with no external forces, the total momentum remains constant. This principle is fundamental in analyzing collisions, as it allows us to equate the total momentum before and after an event. In this scenario, calculating the net momentum components helps in understanding how the vehicles will interact at the intersection.