Here's one possibility using titlesec, tikz and fancyhdr. The code needs three runs to stabilize:
\documentclass{book}
\usepackage[margin=2.5cm,centering]{geometry}
\usepackage{lmodern}
\usepackage{tikz}
\usepackage{emptypage}
\usepackage{fancyhdr}
\usepackage{multicol}
\usepackage[explicit]{titlesec}
\usepackage{lipsum}
\definecolor{color2}{RGB}{255,197,51}
\definecolor{color3}{RGB}{121,163,65}
\definecolor{color1}{RGB}{53,78,85}
\definecolor{color4}{RGB}{0,27,92}
% page style - headers and footers
\pagestyle{fancy}
\fancyheadoffset[L,R]{2.5cm}
\renewcommand\headrulewidth{0pt}
\fancyhf{}
\fancyhead[EL]{%
\begin{tikzpicture}[remember picture,overlay]
\node[
inner sep=0pt,
fill=\chapterbackcolor,
font=\fontsize{40}{48}\selectfont\color{white}\sffamily,
text width=1.5cm,
anchor=south west,
text height=1.5cm,
text depth=0.2cm,
align=center
]
(chapnum)
{\thechapter};
\node[
fill=\chapterbackcolor,
anchor=south west,
font=\color{white}\sffamily
]
(mark)
at ([xshift=1em]chapnum.south east)
{\leftmark};
\draw[\chapterbackcolor,line width=1pt]
([xshift=1em]mark.south east) -- ++(\paperwidth,0);
\end{tikzpicture}%
}
\fancyhead[OL]{%
\begin{tikzpicture}[remember picture,overlay]
\node[
inner sep=0pt,
fill=\chapterbackcolor,
font=\fontsize{40}{48}\selectfont\color{white}\sffamily,
anchor=north east,
align=center
]
(chapimage)
at (current page.north east)
{\includegraphics[height=1.5cm,width=4cm]{example-image-a}};
\node[
inner sep=0pt,
anchor=south east,
font=\color{\chapterbackcolor}\sffamily
]
(mark)
at ([xshift=-1em]chapimage.south west)
{\rightmark};
\draw[\chapterbackcolor,line width=1pt]
([yshift=-1.5ex]mark.south east) -- ++(-\paperwidth,0);
\end{tikzpicture}%
}
\fancyfoot[EL]{%
\begin{tikzpicture}[remember picture,overlay]
\node[
text width=2cm,
text height=0.5cm,
text depth=1.5cm,
fill=\chapterbackcolor!20,
font=\Large\sffamily,
anchor=north east,
align=center
]
{\thepage};
\end{tikzpicture}
}
\fancyfoot[OR]{%
\begin{tikzpicture}[remember picture,overlay]
\node[
text width=2cm,
text height=0.5cm,
text depth=1.5cm,
fill=\chapterbackcolor!20,
font=\Large\sffamily,
anchor=north west,
align=center
]
{\thepage};
\end{tikzpicture}
}
\renewcommand{\chaptermark}[1]{\markboth{\MakeUppercase{#1}}{}}
\renewcommand{\sectionmark}[1]{\markright{\thesection.\ \MakeUppercase{#1}}}
% chapter style
\newcommand\chapterbackcolor{}
\renewcommand\chapterbackcolor{%
\ifcase\value{chapter}color4\or color1\or color2\else color3\fi}
\makeatletter
\newcommand\introduction[1]{\def\@introduction{#1}}
\titleformat{\chapter}[block]
{\normalfont\Large\bfseries\sffamily}
{}
{0em}
{%
\begin{tikzpicture}[remember picture,overlay]
\node[fill=\chapterbackcolor,text width=\paperwidth,anchor=north,minimum height=7cm]
(titleback)
at (current page.north)
{};
\node[font=\huge\color{white},anchor=north west]
(title)
at ([xshift=1cm,yshift=-1cm]titleback.north west)
{{\fontsize{40}{48}\selectfont\thechapter}\quad\MakeUppercase{#1}};
\node[fill=white,anchor=north west,rounded corners,text width=\the\dimexpr\paperwidth-2cm\relax]
(intro)
at ([yshift=-0.5cm]title.south west)
{Introduction\\\vspace*{-.35\baselineskip}%
\begin{minipage}[c][2.2cm][c]{\linewidth}
\begin{multicols}{2}
\normalfont\normalsize\@introduction
\end{multicols}
\end{minipage}%
};
\end{tikzpicture}%
}
\titleformat{name=\chapter,numberless}[block]
{\normalfont\Large\bfseries\sffamily}
{}
{0em}
{%
\begin{tikzpicture}[remember picture,overlay]
\node[fill=\chapterbackcolor,text width=\paperwidth,anchor=north,minimum height=7cm]
(titleback)
at (current page.north)
{};
\node[font=\huge\color{white},anchor=north west]
(title)
at ([xshift=1cm,yshift=-1cm]titleback.north west)
{\MakeUppercase{#1}};
\end{tikzpicture}%
}
\makeatother
\titlespacing*{\chapter}
{0pt}{0pt}{5cm}
\newcommand\Text{% dummy text just for the example
Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus
tincidunt ultrices. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. In
hac habitasse platea \columnbreak dictumst. Integer tempus convallis augue. Etiam facilisis.
Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed
gravida sollicitudin, felis odio placerat quam, ac pulvinar elit purus eget enim.
}
\begin{document}
\mbox{}\thispagestyle{empty}\clearpage% just for the example
\tableofcontents
\introduction{\Text}
\chapter{circular motion and gravitation}
\section{Circular motion}
\lipsum[1-28]
\introduction{\Text}
\chapter{circular motion and gravitation}
\section{Circular motion}
\lipsum[1-28]
\introduction{\Text}
\chapter{circular motion and gravitation}
\section{Circular motion}
\lipsum[1-18]
\end{document}

The different colors are selected using a \chapterbackcolor command that takes its values using a simple \ifcase on the value of the chapter counter; colors have been defined using \definecolor from the xcolor package; in its actual form, there's only four colors: one to be used for unnumbered chapters and the other three for the first three numbered chapters. One can simply define more colors and add them in the \ifcase clause for more chapters:
\definecolor{color2}{RGB}{255,197,51}
\definecolor{color3}{RGB}{121,163,65}
\definecolor{color1}{RGB}{53,78,85}
\definecolor{color4}{RGB}{0,27,92}
\renewcommand\chapterbackcolor{%
\ifcase\value{chapter}color4\or color1\or color2\else color3\fi}
All the elements of the chapter titles and the headers were designed basically placing the elements at desired locations using \nodes inside a tikzpicture.
There are still room for improvement: the page numbering for the first page of each chapter (a redefinition of the plain page style easily achieved using fancyhdr features), a way to change the header image from chapter to chapter but compared to what has been done up to this point, those are easy tasks.