/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 A vector is \(20.0 \mathrm{m}\) ... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 13

A vector is \(20.0 \mathrm{m}\) long and makes an angle of $60.0^{\circ} \mathrm{coun}-\( terclockwise from the \)y\( -axis (on the side of the \)-x$ -axis). What are the \(x\) - and \(y\) -components of this vector?

Short Answer

Expert verified
Answer: The x-component of the vector is -10.0 m, and the y-component is 17.32 m.

Step by step solution

01

Determine the reference angle

To find the x and y components, first, we need to find the reference angle from the -x-axis. Since the angle is measured counterclockwise from the y-axis, we know that: Reference angle = \((180^{\circ} - 60^{\circ})= 120^{\circ}\)
02

Find the x- and y-component using trigonometric functions

Trigonometric functions can be used to find the x- and y-components of the vector. For x-component, \( \textit{x} = \textit{magnitude} \times \textit{cos(reference angle)}\) For y-component, \( \textit{y} = \textit{magnitude} \times \textit{sin(reference angle)}\)
03

Calculate the x-component

Using the formula for x-component, and given magnitude, and reference angle: x = \(20.0 \ (\textit{m}) \times \textit{cos(120掳)}\) x-component = \(20.0 \ (\textit{m}) \times -0.5\) (Note that the cos(120掳) = -0.5) x-component = \(-10.0 \mathrm{m}\)
04

Calculate the y-component

Using the formula for y-component, and given magnitude, and reference angle: y = \(20.0 \ (\textit{m}) \times \textit{sin(120掳)}\) y-component = \(20.0 \ (\textit{m}) \times 0.866\) (Note that the sin(120掳) = 0.866) y-component = \(17.32 \mathrm{m}\)
05

Report the components

The x-component of the vector is -10.0 m and the y-component is 17.32 m.

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Most popular questions from this chapter

An African swallow carrying a very small coconut is flying horizontally with a speed of \(18 \mathrm{m} / \mathrm{s}\). (a) If it drops the coconut from a height of \(100 \mathrm{m}\) above the Earth, how long will it take before the coconut strikes the ground? (b) At what horizontal distance from the release point will the coconut strike the ground?
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