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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 22: Races "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.1, Page number 22.3"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "A's time over the course is 241.0 sec\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "bt=9; #beat time(sec)\n",
+ "st=0; #start time(sec)\n",
+ "bd=36; #beat distance(m)\n",
+ "sd=0; #start distance(m)\n",
+ "L=1000-36; #loser's distance(m)\n",
+ "\n",
+ "#Calculation\n",
+ "At=(bt+st)*L/(bd+sd); #A's time over the course(sec)\n",
+ "\n",
+ "#Result\n",
+ "print \"A's time over the course is\",At,\"sec\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.2, Page number 22.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "length of race of winning post is 120.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "V=1; #assume\n",
+ "A=4/3; #speed of A relative to B\n",
+ "d=30; #distance(m)\n",
+ "\n",
+ "#Calculation\n",
+ "L=d/(V-(1/A)); #length of race of winning post(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"length of race of winning post is\",L,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.3, Page number 22.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "start distance is 40.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "bt=0; #beat time(sec)\n",
+ "st=10; #start time(sec)\n",
+ "bd=0; #beat distance(m)\n",
+ "L=250; #loser's distance(m)\n",
+ "W=1000; #winner's distance(m)\n",
+ "\n",
+ "#Calculation\n",
+ "x=L/W;\n",
+ "sd=((bt+st)/x)-bd; #start distance(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"start distance is\",sd,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.4, Page number 22.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "beat distance is 3.33 m\n",
+ "answer given in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "bt=10; #beat time(sec)\n",
+ "st=0; #start time(sec)\n",
+ "sd=0; #start distance(m)\n",
+ "L=300; #loser's distance(m)\n",
+ "W=100; #winner's distance(m)\n",
+ "\n",
+ "#Calculation\n",
+ "x=L/W;\n",
+ "bd=((bt+st)/x)-sd; #beat distance(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"beat distance is\",round(bd,2),\"m\"\n",
+ "print \"answer given in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.5, Page number 22.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "C would beat B by 2.04 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=100; #length of race(m)\n",
+ "x12=2; #A beats C by(m)\n",
+ "x13=4; #A beats B by(m)\n",
+ "\n",
+ "#Calculation\n",
+ "x23=L*(x13-x12)/(L-x12); #C would beat B by(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"C would beat B by\",round(x23,2),\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.6, Page number 22.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "C would beat B by 20.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=1000; #length of race(m)\n",
+ "x12=50; #A beats C by(m)\n",
+ "x13=69; #A beats B by(m)\n",
+ "\n",
+ "#Calculation\n",
+ "x23=L*(x13-x12)/(L-x12); #C would beat B by(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"C would beat B by\",x23,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.7, Page number 22.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed of B is 1.6 m/s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Ad=100; #distance of A(m)\n",
+ "Bd=Ad-4; #distance of B(m)\n",
+ "As=2; #speed of A(m/s)\n",
+ "bt=10; #beat time(sec)\n",
+ "st=0; #start time(sec)\n",
+ "\n",
+ "#Calculation\n",
+ "t=bt+st;\n",
+ "Bs=Bd/(t+(Ad/As)); #speed of B(m/s)\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of B is\",Bs,\"m/s\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.8, Page number 22.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "B wins by 1.0 s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Bd=330; #distance of B(m)\n",
+ "Bt=44; #time of B(sec)\n",
+ "sd=30; #start distance(m)\n",
+ "A=41; #time taken for A(sec)\n",
+ "\n",
+ "#Calculation\n",
+ "B=Bt*(Bd-sd)/Bd; #time taken for B(sec)\n",
+ "T=A-B; #B wins by(s)\n",
+ "\n",
+ "#Result\n",
+ "print \"B wins by\",T,\"s\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.9, Page number 22.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time taken for A is 24.0 sec\n",
+ "answer given in the book is wrong\n",
+ "time taken for B is 30.0 sec\n",
+ "time taken for C is 32.0 sec\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=200; #length of race(m)\n",
+ "x12=40; #A beats C by(m)\n",
+ "x13=50; #A beats B by(m)\n",
+ "Tc=2; #time for C(sec)\n",
+ "\n",
+ "#Calculation\n",
+ "x23=L*(x13-x12)/(L-x12); #C would beat B by(m)\n",
+ "C=Tc*L/x23; #time taken for C(sec)\n",
+ "B=C-Tc; #time taken for B(sec)\n",
+ "A=B*(L-x12)/L; #time taken for A(sec)\n",
+ "\n",
+ "#Result\n",
+ "print \"time taken for A is\",A,\"sec\"\n",
+ "print \"answer given in the book is wrong\"\n",
+ "print \"time taken for B is\",B,\"sec\"\n",
+ "print \"time taken for C is\",C,\"sec\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.10, Page number 22.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "A can give C a start of 64.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=1000; #length of race(m)\n",
+ "x12=40; #A beats C by(m)\n",
+ "x23=25; #A beats B by(m)\n",
+ "\n",
+ "#Calculation\n",
+ "x13=(x23*(L-x12)/L)+x12; #A can give C a start of(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"A can give C a start of\",x13,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.11, Page number 22.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "A will beat C by 58.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=400; #length of race(m)\n",
+ "L1=600; #full length of race(m)\n",
+ "L2=500; #length of another race(m)\n",
+ "x12=60; #A beats B by(m)\n",
+ "x23=25; #A beats C by(m)\n",
+ "\n",
+ "#Calculation\n",
+ "x12=x12*L/L1; #A beats B by(m)\n",
+ "x23=x23*L/L2; #A beats C by(m)\n",
+ "x13=(x23*(L-x12)/L)+x12; #A will beat C by(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"A will beat C by\",x13,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 22.12, Page number 22.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed of A is 8.0 m/s\n",
+ "speed of B is 7.0 m/s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=400; #length of race(m)\n",
+ "Bt1=50/7; #time taken by B more than A(sec)\n",
+ "Bt2=5; #time taken by B with lesser distance(sec)\n",
+ "d=15; #lesser distance(m)\n",
+ "\n",
+ "#Calculation\n",
+ "Bt=Bt1-Bt2; #time taken for B(sec)\n",
+ "Bs=d/Bt; #speed of B(m/s)\n",
+ "VA=L/((L/Bs)-Bt1); #speed of A(m/s)\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of A is\",VA,\"m/s\"\n",
+ "print \"speed of B is\",Bs,\"m/s\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2024-12-20 04:49:31 +0000