Explanation

(b) [image:3_image210.emf]
Let ${\overrightarrow{v}}_{t}$= actual velocity of train
${\overrightarrow{v}}_{t}$= actual velocity of car
$\therefore\ {\overrightarrow{v}}_{tc}$= relative velocity of train with respect to car
$\therefore\ {\overrightarrow{v}}_{c}$=25$\widehat{i}$
and ${\overrightarrow{v}}_{tc}$=25$\sqrt{3}\ \widehat{j}$
$\therefore\ \ {\overrightarrow{v}}_{tc} = {\overrightarrow{v}}_{t} - {\overrightarrow{v}}_{c}$
$\therefore\ \ {\overrightarrow{v}}_{t} = {\overrightarrow{v}}_{tc} + {\overrightarrow{v}}_{c}$
= 25$\sqrt{3}\widehat{j}$+25$\widehat{i}$
$v_{t} = \sqrt{\left( 25\sqrt{3} \right)^{2} + (25)^{2}}$
$= 25\sqrt{4}\ $= 50$kmh^{- 1}$