Vectors Physics Example 3

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Example 3

medium
A force of 50 N50 \text{ N} acts at 60°60° above the horizontal. Find the horizontal and vertical components.

Solution

  1. 1
    Horizontal component: Fx=Fcos⁡θ=50cos⁡60°=50×0.5=25 NF_x = F\cos\theta = 50\cos 60° = 50 \times 0.5 = 25 \text{ N}
  2. 2
    Vertical component: Fy=Fsin⁡θ=50sin⁡60°=50×0.866=43.3 NF_y = F\sin\theta = 50\sin 60° = 50 \times 0.866 = 43.3 \text{ N}

Answer

Fx=25 N,Fy=43.3 NF_x = 25 \text{ N}, \quad F_y = 43.3 \text{ N}
Resolving a vector into components is the reverse of finding magnitude and direction. The horizontal component uses cosine, and the vertical component uses sine.

About Vectors

Mathematical quantities that possess both a magnitude (size) and a direction, represented graphically as arrows.

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More Vectors Examples

Example 1 easy

Find the magnitude and direction of the vector with components [formula] and [formula].

Example 2 medium

Add the vectors: [formula] at [formula] (east) and [formula] at [formula] (north). Find the resultan

Example 4 medium

Two forces act on an object: [formula] east and [formula] north. Find the magnitude and direction of

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