If a child pulls a sled through the snow on a level path with a force of 70 N exerted at an angle...

Question:

If a child pulls a sled through the snow on a level path with a force of 70 N exerted at an angle of 38{eq}^\circ {/eq} above the horizontal, find the horizontal and vertical components of the force.

Vector Components

A vector has both a magnitude and direction. If this direction doesn't lie along a perfectly horizontal or vertical direction, we can find the horizontal and vertical components of the vector by using trigonometry on a right triangle where this force is the hypotenuse.

Answer and Explanation:

We can model this force as a right triangle, since we have both an angle and a magnitude. We can assign the value of 70 to the hypotenuse of this triangle, and we can use the angle of 38 degrees in our trigonometric functions. This is the angle made with the horizontal, or x-axis, so that would make the horizontal component the adjacent side and the vertical component the opposite side of this triangle.

We can use the following trigonometric ratios involving sine and cosine to find the components of this force.

{eq}\cos 38^{\circ} = \frac{x}{70}\\ \rightarrow x = 70\cos 38^{\circ} \approx 55.1608\\ \sin 38^{\circ} = \frac{y}{70}\\ \rightarrow y = 70 \sin 38^{\circ} \approx 43.0963 {/eq}


Thus, the horizontal component of this force is 55.16N and the vertical component is 43.10N.


Learn more about this topic:

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Vector Components: The Direction of a Vector

from UExcel Physics: Study Guide & Test Prep

Chapter 2 / Lesson 9
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