Two cars, one traveling north and one traveling west, collide at an intersection.The resulting momentum of the two cars together after the collision is 32 000 kg . m/s N30degreesW.
Find the momentum of each car before the collision.
First we have to understand that physical quantities have no effect to their perpendicular directions.
As North and West are also perpendicular just by dividing the resulting momentum in to North and West directions you get the momentum s of the cars traveling North and West respectively.
So for the car traveling North direction the momentum before collision would be 32000 cos30 = 16000√3 kg m/s and for the car traveling North direction the momentum before collision would be 32000 sin30 = 16000 kg m/s.
To find the momentum of each car before the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
Let's break down the given information:
1. The resulting momentum of the two cars together after the collision is 32,000 kg·m/s N30degreesW.
Now, let's analyze the information that has been provided:
1. The momentum is given in vector form (N30degreesW), which specifies both the magnitude and direction of the momentum.
To find the momentum of each car before the collision, we need to resolve the given vector momentum into its horizontal and vertical components.
Step 1: Resolve the vector momentum into horizontal and vertical components:
- The momentum vector N30degreesW can be resolved into its horizontal (north-south) and vertical (east-west) components using trigonometry.
The horizontal component (north-south) can be calculated using the formula:
horizontal component = magnitude × cos(angle)
The vertical component (east-west) can be calculated using the formula:
vertical component = magnitude × sin(angle)
Substituting the given values:
horizontal component = 32,000 × cos(30°)
vertical component = 32,000 × sin(30°)
Step 2: Calculate the momentum of each car before the collision:
- Since the law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, the momentum of each car before the collision should be equal to the resolved components calculated in Step 1.
Car traveling north: The momentum of the car traveling north before the collision is equal to the horizontal component, which is 32,000 × cos(30°).
Car traveling west: The momentum of the car traveling west before the collision is equal to the vertical component, which is 32,000 × sin(30°).
Solving these equations will give you the momentum of each car before the collision.