Question

Two forces acting on a particle in opposite directions have the resultant of 10N. If they act at right angles to each other, the resultant it 50N. Fing the 2 forces.

Answer 1

Let the forces be X and Y Newton.

So when the forces are acting in opposite direction we have : X - Y = 10 Newton

Again when the forces are acting at right angles we have : Squared root(X^2 + Y^2 +2*X*Y*cos90) =50 Newton.

Or, X^2 + Y^2=2500

Putting the first equation here we have,

(Y+10)^2 + Y^2=2500

Solving this we get Y=30 Newton

Therefore, X=(10+Y)=10+30=40 Newton.

Hence the two forces are 30 and 40 Newton.

Answer 2

Answer:

Let the two vectors be A and B.

A = 40N. B = 30N.

Explanation:

So, if they are in opposite direction means A - B = 10( as given in the ques.)

also , A² + B² = 50² = 2500.

Now ,

(A  + B)² = A² + B² +2AB

(A - B)² =  A² + B² - 2AB

(A + B) ² + (A  - B)² = 2(A² + B²)

Now subsitute the values

(A + B)² + 100 = 2 × 2500

(A + B)² = 4900

A + B = √4900 = 70

A + B = 70

A - B = 10

Now add these equations ,

   A + B = 70

 +A - B = 10

____________

2A = 80

A = 40N

B = (70 - 40) = 30N.

Hope it helps . All the best .

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