Vectors Physics Example 4

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Example 4

medium
Two forces act on an object: F⃗1=8 N\vec{F}_1 = 8 \text{ N} east and F⃗2=6 N\vec{F}_2 = 6 \text{ N} north. Find the magnitude and direction of the resultant force.

Solution

  1. 1
    The forces are perpendicular, so: FR=82+62=64+36=100=10 NF_R = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \text{ N}.
  2. 2
    Direction: θ=tan⁡−1(68)=tan⁡−1(0.75)≈36.9°\theta = \tan^{-1}\left(\frac{6}{8}\right) = \tan^{-1}(0.75) \approx 36.9° north of east.

Answer

FR=10 N at 36.9° north of eastF_R = 10 \text{ N at } 36.9° \text{ north of east}
Perpendicular vectors combine using the Pythagorean theorem. The direction is found with inverse tangent. This 6-8-10 triangle is a scaled 3-4-5 right triangle.

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 3 medium

A force of [formula] acts at [formula] above the horizontal. Find the horizontal and vertical compon

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