# A laser pointer is kept at a constant and fixed height above the floor, but it can

## Question:

A laser pointer is kept at a constant and fixed height above the floor, but it can move horizontally back and forth in a straight line. A mirror is placed on a platform at a fixed distance from a wall at a fixed height parallel to the floor. The goal of this project is to *find the distance that the laser pointer must be away from the wall so that when the beam is reflected off the mirror, it will hit a target that is 1.25 meters off the ground*, as shown below.

Distance from the wall to the center of the mirror: 130 cm

Height of the laser pointer: 120 cm

Height of the mirror to the floor: 24 cm

These values remain constant during the project.

The laser pointer is then set up at five different positions so that the beam is reflected off the center of the mirror and reflected onto the wall. At each position, the distance of the laser pointer from the wall and the height of the reflected beam on the wall is measured and recorded.

Distance from the wall to the laser pointer. (x) | 194 cm | 206 cm | 221 cm | 377 cm | 441 cm |

Distance from the floor to the reflection point on the wall (y) | 224 cm | 195 cm | 168 cm | 76 cm | 66 cm |

**Instructions/Procedure**

Use the given data to:

- Graph the data (you are encouraged to use excel, demos, or google sheets). Be sure to label the axes and use appropriate units)
- Use the given information about the 5 different placements of the mirror to determine the values of 'b' and 'c' in the equation. Explain your work.
- Use the data values, your equation, and your graph to approximate the value of 'a' in the equation:

. Explain your work.

- Graph the data points and your equation from step 3 on a graph (use graphing software such as desmos.com). You know you have done this correctly when you see your equation passing very close to the data points.
- Use your equation to answer the question
*How far away from the wall should the laser pointer be to hit the target that is 1 meter (100 cm) up on the wall.* - Write your equation in form. Identify the vertical and horizontal asymptotes. Explain.

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