3.2 Exercises for basic mathematical operations

shows a Sharp GP2D12 infrared distance sensor and a BasicX-24 microprocessor .

Distance sensor and processor

The distance sensor uses a beam of infrared light to measure the distance from the sensor to an object; the sensor provides an output voltage that has a fairly complicated relationship to this distance. The BasicX processor converts the voltage from the sensor into a number between zero and one. Let us denote this number as $x$ , and the distance (measured in inches) between the sensor and object as $d$ . The relationship between $x$ and $d$ is Compute the value of $d$ for the following values of $x$ :

• $x=0.10$
• $x=0.15$
• $x=0.20$

The terminal velocity reached by a sky diver depends on many factors, including their weight, their body position as they fall, and the density of the air through which they fall. The terminal velocity is given by

where

• $m$ is the sky diver's mass
• $g$ is Earth's gravitational constant
• $r$ is the atmospheric density
• $A$ is the sky diver's effective area
• $C_d$ is the sky diver's coefficient of drag

Compute the terminal velocity of the sky diver for each of the following values of $m$ :

• $m=40\; kg$
• $m=80\; kg$
• $m=120\; kg$

Use the following values for the other variables:

• $g=9.8$
• $r=1.2$
• $A=0.5$
• $C_d=1$