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Two forces of 100 N and 40 N are acting on a car.

a.) What is the maximum resultant force on the car?  At what angle would this occur?

b.) What is the minimum resultant force on the car?  At what angle would this occur?

c.) What is the range of forces that can be applied to the car?

d.) Can a force of 30 N possibly be attained with these two forces?

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using cosine rule for these 2 forces at an angle x ,c is resultant, a and b are the 2 other forces,

c = sqrt(a^2+b^2-2abcosx)

a. becomes maximum when cosx =0 or x=90degrees.

c = sqrt(100^2 + 40^2 -2x100x40Cos90)

c = 107.7 N as resultant

b. becomes minimum when cosx =1 or x=0 degrees.

c =sqrt(100^2 + 40^2 -2x100x40Cos0)

c = 60 N as resultant

c. Range of forces will be from 60 N up to 107.7 N

d. It can not, because it is not within the range.

= sqrt(100^2 + 40^2 -2x100x40Cos0

= 60 N
by Diamond (39,704 points)

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