Forming a differential equation for a body whose mass changes

In summary, the ejected mass has a speed of v-u at the start of the interval because it is being ejected relative to the body it is being ejected from. To an outside observer, the speed would appear as v+u since the body and the mass are moving in the same direction. The change in mass, represented by delta m, does not necessarily mean an addition of mass, but rather a change in mass at a different time t'.
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I was having trouble following various aspects of the above explanation:

Why does the ejected mass have a speed "v-u" at the start of the interval?

Why is the oif the body mass (m + (Delta)m) and not (m - (Delta)m).

Thanks
 
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The speed has to be v-u since the mass is being ejected relative to the body it is being ejected from. To an outside observer it would be v+u since the mas and the body are apparently going in the same direction.

"Why is the oif the body mass (m + (Delta)m) and not (m - (Delta)m)."

As the body moves the mass changes [tex]\delta m[/tex] doesn't necessarily means mass is added...simply means a change in mass at another time t
 
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Related to Forming a differential equation for a body whose mass changes

What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model and predict the behavior of physical systems, including those that involve changing mass.

Why is a differential equation needed to describe a body with changing mass?

A differential equation is needed because it takes into account the rate at which a body's mass is changing, which is an important factor in determining its overall behavior. Without a differential equation, the model would not accurately represent the dynamics of the body.

What factors are included in a differential equation for a body with changing mass?

A differential equation for a body with changing mass includes variables such as the body's mass, its acceleration, and any external forces acting on it. These factors are all important in determining the body's motion.

How is a differential equation for a body with changing mass derived?

A differential equation for a body with changing mass is derived by applying Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. This equation can then be rearranged to solve for the acceleration.

What are some real-life applications of differential equations for bodies with changing mass?

Differential equations for bodies with changing mass are used in a variety of fields, including physics, engineering, and biology. They can be used to model the motion of objects under the influence of gravity, the behavior of chemical reactions, and the growth and development of living organisms.

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