A train is moving due east and a car is moving due north, both with the same speed $40 \mathrm{~km}

Question

A train is moving due east and a car is moving due north, both with the same speed $40 \mathrm{~km} / \mathrm{h}$. What is the observed speed of motion of car to the passenger in the train?

Professor PC Thomas Classes · Answer

(c) : Velocity of train $\vec{v}_T=40 \hat{i} \mathrm{~km} / \mathrm{h}$ Velocity of car, $$ \vec{v}_C=40 \hat{j} \mathrm{~km} / \mathrm{h} $$ Velocity of car with respect to train, $$ \begin{aligned} & \vec{v}_{G T}=\vec{v}_G-\vec{v}_T=40 \hat{j}-40 \hat{i} \ & =(-40 \hat{i}+40 \hat{j}) \mathrm{km} / \mathrm{h} \end{aligned} $$ Speed of car with respect to train, $ \ \left|\vec{v}_{C T}ight|=\sqrt{40^2+40^2}=40 \sqrt{2} \mathrm{~km} / \mathrm{h} $