Question

The force of gravity between two objects is given by  Fg =

−Gm1m2
r2
, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the objects' centers. Find the vertical asymptote of the graph of the function and explain its meaning in context.

Answer 1

The vertical asymptote of the graph of the function representing the force of gravity between two objects is when the distance between the objects' centers, denoted as 'r', approaches zero. This means that as the objects get closer and closer together, the force of gravity becomes infinitely large.

Step-by-step explanation:

The vertical asymptote of the graph of the function representing the force of gravity between two objects is when the distance between the objects' centers, denoted as 'r', approaches zero. This means that as the objects get closer and closer together, the force of gravity becomes infinitely large. In other words, there is no limit to how strong the gravitational force can become as the distance between objects tends to zero.

Physically, this means that if two objects are very close to each other, the force of gravity between them becomes extremely strong, which can result in a significant acceleration of the objects towards each other.

Answer 2

Answer with explanation:

The force of gravity between two objects is given by

`F_(g)=(-Gm_(1)m_(2))/(r^2)`

Replacing , force by , y and product of -G the gravitational constant, masses
`m_(1), m_(2)` by t,the above equation reduces to,

`y=(t)/(x^2)`

Horizontal Asymptote, is, y=0

`y= \lim_(x \to \infty) f(x)\\\\y = \lim_(x \to \infty) (1)/(x^2)\\\\y=0`

And Vertical Asymptote is, x=0

`x= \lim_(y \to \infty) f(y)\\\\x = \lim_(y \to \infty) (-1)/(√(y))\\\\x=0`

The meaning of vertical asymptote in context of the graph of the function is ,that when Distance between two objects reduces to Zero, the force of attraction between two bodies, reduces to zero.