Question

An "inverted V" antenna is used in areas of limited space as it can significantly reduce the ground footprint of the antenna without significantly impacting performance. Your neighbor is an amateur radio enthusiast who has such an antenna. The antenna is anchored two feet above the ground on the sides and to a 20 -foot tall mast 12 feet away. Write the equation that describes this situation, assuming the origin is on the ground beneath the anchor point on the left side of the antenna. \[ y=a|x-h|+k \]

Answer 1

In this situation, the "inverted V" antenna can be described by the equation you provided:

�

=

�

⋅

∣

�

−

ℎ

∣

+

�

y=a⋅∣x−h∣+k

Let's break down the terms in the equation:

�

y: This represents the height above the ground of the antenna at a given horizontal position

�

x.

�

a: This is a coefficient that determines the shape and scaling of the antenna.

�

x: This is the horizontal position along the ground.

ℎ

h: This is the horizontal position (distance) where the antenna is anchored on the ground.

�

k: This is the vertical shift or offset of the antenna from the ground at the anchor point.

In this scenario:

The antenna is anchored two feet above the ground on the sides, so

�

=

2

k=2.

The antenna is anchored 12 feet away from the origin (on the left side), so

ℎ

=

12

h=12.

The specific value of

�

a depends on the characteristics of the antenna and how it's configured. If you have the value of

�

a, you can substitute it into the equation to complete the description of the "inverted V" antenna in your neighbor's setup

Explanation: