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Exercises for Basic Mathematical Operations

Module by: Darryl Morrell. E-mail the author

Summary: This module has exercises on using mathematical operations in m-file scripting environments.

Exercise 1

Figure 1 shows a Sharp GP2D12 infrared distance sensor and a BasicX-24 microprocessor.

Figure 1: The infrared distance sensor and microprocessor.
Distance Sensor and Processor
Distance Sensor and Processor (IRProcessor.png)
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 xx, and the distance (measured in inches) between the sensor and object as dd. The relationship between xx and dd is
d=34.63x−5.1622.54 d 34.63 x 5.162 2.54
(1)
Compute the value of dd for the following values of xx:
  • x=0.10x0.10
  • x=0.15x0.15
  • x=0.20x0.20

Exercise 2

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

V t =2⁢m⁢gr⁢A⁢ C d V t 2 m g r A C d
(2)
where
  • mm is the sky diver's mass
  • gg is Earth's gravitational constant
  • rr is the atmospheric density
  • AA is the sky diver's effective area
  • C d 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 mm:
  • m=40 kgm40 kg
  • m=80 kgm80 kg
  • m=120 kgm120 kg
Use the following values for the other variables:
  • g=9.8g9.8
  • r=1.2r1.2
  • A=0.5A0.5
  • C d =1 C d 1

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