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Chapter 2: Problem 1

(a) Write a script that calculates the number of seconds, \(s\), given the number of hours, \(h\), according to the formula \(s=3600 h\). (b) Use the script to find the number of seconds in \(1.5,12\) and \(24 \mathrm{~h}\).

Short Answer

Expert verified
1.5 hours is 5400 seconds, 12 hours is 43200 seconds, and 24 hours is 86400 seconds.

Step by step solution

01

- Understand the Formula

The formula provided to calculate the number of seconds given the number of hours is: o s = 3600 ho where, s is the number of seconds and h is the number of hours.
02

- Write the Script

Use a programming language to write a script that applies the formula to convert hours into seconds. Here is an example in Python:```python# Function to convert hours to secondsdef hours_to_seconds(hours): return 3600 * hours# Example valuestest_hours = [1.5, 12, 24]# Calculating seconds for each valuefor h in test_hours: print(f'{h} hours is {hours_to_seconds(h)} seconds')```
03

- Use the Script

Run the script to find the number of seconds for 1.5 hours, 12 hours, and 24 hours. The output will be:1.5 hours is 5400 seconds12 hours is 43200 seconds24 hours is 86400 seconds

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Basic Python Scripting
Python is a versatile and beginner-friendly programming language. It’s great for learning how to code because its syntax is clear and intuitive. When writing basic Python scripts, you’ll often start with defining a function. Functions in Python allow you to define reusable pieces of code. In the provided exercise, we define a function to convert hours to seconds.
Unit Conversion
Unit conversion is a fundamental concept in programming and in many scientific fields. It allows you to convert measurements from one unit to another. In the context of this exercise, we’re converting hours to seconds. The conversion formula is straightforward because we know that one hour is equal to 3600 seconds.
Coding Exercises
Coding exercises like this one are an excellent way to practice and improve your programming skills. They offer hands-on experience with real-world problems. When tackling coding exercises, it’s helpful to follow these steps:

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Most popular questions from this chapter

(a) Write a function that returns the two-dimensional unit vector, \(\left(u_{x}, u_{y}\right)\), corresponding to an angle \(\theta\) with the \(x\)-axis. You can use the formula \(\left(u_{x}, u_{y}\right)=\) \((\cos \theta, \sin \theta)\), where \(\theta\) is given in radians. (b) Find the unit vectors for \(\theta=0, \pi / 6, \pi / 3, \pi / 2,3 \pi / 2\). (c) Rewrite the function to instead take the argument \(\theta\) in degrees.

The file trajectory.dat \({ }^{4}\) contains a list of numbers: to \(x 0 \quad y 0\) t1 \(x 1 y 1\) \(\begin{array}{lll}\cdots & \cdots & \cdots \\ \operatorname{tn} & \mathrm{xn} & \mathrm{yn}\end{array}\) corresponding to the time \(t(i)\) measured in seconds, and the \(x\) and \(y\) positions \(x\) (i) and \(y\) (i) measured in meters for the trajectory of a projectile. (a) Read the data file into the arrays ' \(\mathrm{t}, \mathrm{x}\), and \(y\). (b) Plot the \(x\) and \(y\) positions as function of time in two plots above each other. (c) Plot the \((x, y)\) position of the object in a plot with \(x\) and \(y\) on the two axes.

The iterative mapping \(x(i+1)=r x(i)(1-x(i))\) is called the logistic map. (a) Make a function logistic \((\mathrm{x}, \mathrm{r})\) which returns the value of \(x(i+1)\) given \(x(i)\) and \(r\) as inputs. (b) Write a script with a loop to calculate the first 100 steps of the logistic map starting from \(x(1)=0.5\). Store all the values in an array \(\mathrm{x}\) with \(n=100\) elements and plot \(x\) as a function of the number of steps \(i\) : (c) Explore the logistic map for \(r=1.0,2.0,3.0\) and \(4.0\).

The function \(f(x ; n)\) is given as \(f(x ; n)=x^{-n}\). (a) Make a function fralue \((\mathrm{x}, \mathrm{n})\) which returns the value of \(f(x ; n)\). (b) Use this function to plot \(1 / x, 1 / x^{2}\) and \(1 / x^{3}\) in the same plot for \(-1

The function \(g(x ; n)\) is given as: $$ g(x ; n)=\frac{\sin (x)}{x^{n}} $$ (a) Make a function gvalue \((\mathrm{x}, \mathrm{n})\) which returns the value of \(g(x ; n)\). (b) Use this function to plot \(\sin (x) / x, \sin (x) / x^{2}\) and \(\sin (x) / x^{3}\) in the same plot for \(-5
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