Question

Two forces 12n and 24n act on abody 90degreecentgrade find resultant force

Answer 1

Question :-

Two forces 12 N and 24 N act on a body at 90° . Find the resultant force.

Answer :-

• 12√5 N

Solution :-

Given -

• A = 12 N

• B = 24 N

• θ = 90°

To Find -

• Resultant

Process -

By triangle law of vector addition,

Resultant

= √[ A² + B² + 2AB cosθ ]

= √[ (12)² + (24)² + 2(12)(24) cos 90° ]

= √[ 144 + 576 + 0 ]

= √[ 720 ]

= √[ 9 × 16 × 5 ]

= 3 × 4 × √5

= 12√5

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Hence, the resultant force has a magnitude of 12√5 N .

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Formulae Used :

Resultant = √[ A² + B² + 2AB cosθ ]

cos 90° = 0

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More About Vectors :

Vector Components -

• A vector has mainly two components which are horizontal and vertical components.

• The value of the horizontal component is cos θ while the value of the vertical component is sin θ.

Vector Multiplication -

There are two ways to multiply vectors which are:

1. Dot Product Of Two Vectors
2. Vector Product

For dot product, the formula is :

A • B = |A| |B| cosθ

For vector product, the formula is :

A × B = |A| |B| sinθ

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Thank You!