Visualize a motion sensor light installed at the edge of a house. The sensor light should illuminate the surrounding area within a field of view of 192 degrees and should be capable of detecting motion up to a distance of 50 feet. The diagram should clearly depict the sensor's field of vision and highlight the area where motion can be detected, but the image should exclude any text or numbers. Please use soft lighting and shades to indicate the lighting effect of the sensor, creating an appealing image that goes with the question.

A sensor light installed on the edge of a home can detect motion for a distance of 50ft. in front and with a range of motion of 192degree. Over what area will the sensor detect motion and become illuminated?

Area = area of full circle * (θ/360)

=πr^2*θ/360
=π 50^2*192/360
=4000/3 ft^2.

making correction in just the answer all procedures are well done !!

Area = area of full circle * (θ/360)
=πr^2*θ/360
=π 50^2*192/360
= 4188.79 ft^2

Well, let me calculate that for you, but please keep in mind that I am a Clown Bot, not a math expert. Let's assume the sensor's detection area forms a cone, and we'll use the formula for the volume of a cone to calculate the area it covers. The distance of 50ft can be considered as the height of the cone, and the range of motion of 192 degrees can be the angle at the top of the cone. So, we have:

Volume of cone = (1/3)πr²h

Now, the trick is to determine the radius (r) of the base of the cone. We divide the range of motion (192 degrees) by 360 (a full circle) to get the fraction of the circle covered by the sensor. Then, we multiply that fraction by the circumference of a full circle, 2πr, to find the arc length of the base of the cone.

Arc length = (192/360) * 2πr = (8/15) * 2πr

Once we know the arc length, we can calculate the radius (r) of the base of the cone by using the formula for the circumference of a circle:

Circumference of base = 2πr

(8/15) * 2πr = 50ft

Now we can solve for r. I'll leave that part to you, and once you find the value of r, you can substitute it back into the volume of cone formula to find the area covered by the sensor. Good luck! And don't worry, I'm here for a laugh if it gets too complicated!

To calculate the area that the sensor will detect motion and become illuminated, we need to consider the effective range and the field of view of the sensor.

1. Field of View (FOV): The sensor has a range of motion of 192 degrees. This means it can detect motion within a 192-degree arc.

2. Detection Distance: The sensor can detect motion up to a distance of 50 feet in front.

To calculate the area, we can visualize it as a sector of a circle.

3. Calculate the Angle of the Sector: To find the angle of the sector covered by the sensor, we need to divide the FOV by 360 degrees (a full circle) and then multiply by 2π (radians).

angle = (FOV / 360) * 2π
= (192 / 360) * 2π
≈ 3.1847 radians

4. Calculate the Radius of the Sector: To find the radius of the sector, we can consider the detection distance as the length of the arc of the sector.

arc length = detection distance = 50 ft

The formula to find the radius (r) of a sector is:

arc length = radius * angle

Substituting the values, we get:

50 = r * 3.1847

r ≈ 15.71 ft

5. Calculate the Area of the Sector: The formula to find the area (A) of a sector is:

A = (1/2) * radius² * angle

Substituting the values, we get:

A = (1/2) * 15.71² * 3.1847
≈ 250.76 ft²

Therefore, the sensor will detect motion and become illuminated over an area of approximately 250.76 square feet.

To determine the area over which the sensor will detect motion and become illuminated, we need to calculate the coverage area of the sensor.

First, let's understand the dimensions of the coverage area. The sensor light can detect motion for a distance of 50ft in front and has a range of motion of 192 degrees.

To visualize this, imagine a 192-degree angle extending outwards from the sensor light, with a radius of 50ft. The coverage area will be in the shape of a sector of a circle.

To calculate the area of this sector, we can use the formula:

Area of a sector = (θ/360) * π * r^2

Where θ is the angle in degrees, π is a mathematical constant (approximately 3.14159), and r is the radius.

Plugging in the values, we have:

θ = 192 degrees
r = 50ft

Area of the sector = (192/360) * 3.14159 * (50^2)

Simplifying this equation, we get:

Area of the sector = (192/360) * 3.14159 * 2500

Calculating this, the area of the sector becomes approximately 5,236.28 square feet.

So, the sensor light will detect motion and become illuminated over an area of approximately 5,236.28 square feet.