Question

A train travelling @66.6 km/hr passes a pole in 9 seconds and platform in 29 seconds what is the length of the platform

Answer 1

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

$\sf\textsf{Given,}$
$\sf\textsf{Speed of the train = 66.6 kmph}$
$\sf\textsf{time taken by the train to cross the pole = 9 s}$
$\sf\textsf{time taken by the train to cross the platform = 29 s}$
$\sf\textsf{Length of the Platform = ?}$

$\underline{\Large{\textsf{Step-1:}}}$
$\sf\textsf{Express the Speed of the train in mps}$

$\sf\textsf{We have,}$
$\bigstar \quad\: \boxed{\mathbf{1 \: kmph =\dfrac{5}{18} \: mps}}$

$\implies \sf\textsf{Speed of the train = 66.6 \times\dfrac{5}{18} mps}$

$\implies \sf\textsf{Speed of the train = 11.1 \times\dfrac{5}{3} mps}$

$\implies \sf\textsf{Speed of the train = \dfrac{55.5}{3} }$

$\implies \sf\textsf{Speed of the train = \dfrac{555}{30} }$

$\implies \sf\textsf{Speed of the train = \dfrac{37}{2} mps}$

$\therefore\: \sf\textsf{Speed of the train =18.5 mps}$



$\underline{\Large{\textsf{Step-2:}}}$
$\sf\textsf{Assume a variable for the Distance covered by the train in passing the Pole}$

$\sf\textsf{Let Distance covered by the train in passing the Pole be d_{1} m}$



$\underline{\Large{\textsf{Step-3:}}}$
$\sf\textsf{Assume a variable for the Distance covered by the train in passing the Platform}$

$\sf\textsf{Let Distance covered by the train in passing the Platform be d_{2} m}$



$\underline{\Large{\textsf{Step-4:}}}$
$\sf\textsf{Find the Length of the train}$

$\sf\textsf{Length of the train is equal to}\\\sf\textsf{the Distance covered by the train in passing the Pole,}\\ \sf\textsf{assuming that the width of the pole is negligible}$

$\sf\textsf{We have,}$
$\bigstar \quad\: \boxed{\mathbf{Speed = \dfrac{Distance\: Covered}{time}}}$

$\sf\textsf{Substituting Values}$

$\implies \sf\textsf{18.5 = \dfrac{d_{1}}{9} }$

$\implies \sf\textsf{ d_{1} = 18.5 \times 9}$

$\implies \sf\textsf{ d_{1} = 166.5 m}$

$\therefore\: \sf\textsf{Length of the train = 166.5 m}$



$\underline{\Large{\textsf{Step-5:}}}$
$\sf\textsf{Find the Distance covered by the train in passing the Platform}$

$\sf\textsf{Distance covered by the train in passing the platform is sum of the lengths of train and Platform}$

$\sf\textsf{From [1]}$

$\sf\textsf{Substituting Values}$

$\implies \sf\textsf{18.5 = \dfrac{d_{2}}{9} }$

$\implies \sf\textsf{ d_{2} = 18.5 \times 29}$

$\implies \sf\textsf{ d_{2} = 536.5 m}$



$\underline{\Large{\textsf{Step-6:}}}$
$\sf\textsf{Find the length of the Platform}$

$\sf\textsf{Subtracting the Length of the train}\\ \sf\textsf{from the Distance covered by the train}\\ \sf\textsf{in passing the platform gives Length of Platform}$

$\implies \sf\textsf{Length of the Platform = d_{2}-d{1} }$

$\sf\textsf{Substituting Values}$

$\implies \sf\textsf{Length of the Platform = 536.5 - 166.5}$

$\implies \sf\textsf{Length of the Platform = 370 m}$

$\therefore$
$\blacksquare\quad \textsf{The Length of the Platform = \underline{\Large{\textbf{370\: m}}}}$