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Chapter 3: Q. 5 (page 77)

5. I A position vector in the first quadrant has an x-component of 6m and a magnitude of 10m . What is the value of its y-component?

Short Answer

Expert verified

y-component = 8 m

Step by step solution

01

Step 1. Given Information

A position vector in the first quadrant has an -component of 6mand a magnitude of 10m.

This can be represented as

The position vector r→whose magnitude r10mis has an x - component of 6 m. It makes an angle θwith the positive x-axis in the first quadrant.

Here;

r→is the position vector

r=10mrx−x-component of the position vector.

rx=6mry−y-component of the position vector.

θ- The angle that the position vector makes with the positive x- axis.

Formula used: x-component,rx=rcosθ

y-component,ry=rsinθ

02

Step 2. Explanation

x-component, rx=rcosθ

Substituting the value of randrxin the relation.

rx=rcosθ6m=10m×cosθcosθ=6m10mθ=cos−1610θ=53.13°

Thus, the y-component is

ry=rsinθ=10m×sin53.13°=7.99m≈8m

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