Derive Linear Momentum: m2(D-c)/(m1+m2)

[ingrida1]

Homework Statement

Derive the above relationship m2(D-c)
X1=---------
m1+m2

Homework Equations

The Attempt at a Solution

 

[berkeman]

Sorry, ingrida1. That would not appear to be enough information for us to help you. Please carefully fill out all three portions of the Homework Help template in your original post. The problem statement should be exactly as stated in your homework set, and you need to fill in the sections on Relevant equations, and your Attempt at a solution.

 

[m2003]

Linear momentum is defined as the product of an object's mass and its velocity. In this case, we have two objects with masses m1 and m2, and they are moving at velocities c and D, respectively. The total linear momentum of the system is given by the sum of the individual momenta of each object. In other words, the linear momentum of the system is equal to the sum of m1*c and m2*D.

To derive the given relationship, we first need to define the variables. Let X1 represent the linear momentum of the system. Then, we can rewrite the equation as:

X1 = m1*c + m2*D

Next, we can factor out the common term of m2 from the second term on the right-hand side of the equation:

X1 = m1*c + m2*(D-c)

We can then rearrange the equation to isolate m2*(D-c) on one side:

m2*(D-c) = X1 - m1*c

Lastly, we can divide both sides by m1+m2 to obtain the final derived relationship:

m2(D-c)/(m1+m2) = (X1 - m1*c)/(m1+m2)

This relationship shows the linear momentum of the system in terms of the individual masses and velocities of the objects. It can also be interpreted as the weighted average of the individual momenta, where the weight of each object is determined by its mass.