You and someone else are pulling on an object with forces of 50N and 75N respectively. If you are allowed to pull in any direction, what range of values is possible for the magnitude of the resultant force ?

You can use the fact that two pulls on one object is minimum if both pulls are oppositely working and is maximum if both the pulls are working in same direction.

The range of values possible for the magnitude of the resultant force is

[25, 125]

What are the directions in which two pulls on the same object become maximum in resultant and minimum in resultant?

Two pulls on one object is minimum if both pulls are oppositely working and is maximum if both the pulls are working in same direction.

Using above conclusion for given pair of forces on one object

For getting minimum value:

Let they are working oppositely, then the resultant force would be subtraction of one force from other

Based on the direction we can have

Resultant force =

[tex]75N - 50N = 25N\\50N - 75N = -25N[/tex]

Since the magnitude is same 25, thus, the minimum magnitude we can get is 25

Let the forces are working in same direction, then we have:

Resultant force = 75N + 50N = 125N

Thus, the maximum resultant force's magnitude is 125

Thus,

The range of values possible for the magnitude of the resultant force is

[25, 125]

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