Question

Ram and Shyam are walking on two perpendicular tracks with speed 3 $ms^{-1}$ and 4 $ms^{-1}$, respectively. At a certain moment (say t = 0 s), Ram and Shyam are at 20 m and 40 m away from the intersection of tracks respectively, and moving towards the intersection of the tracks.

During the motion the magnitude of velocity of ram with respect to Shyam is

• A. 1 $ms^{-1}$
• B. 4 $ms^{-1}$
• C. 5 $ms^{-1}$
• D. 7 $ms^{-1}$

Answer 1

Answer: (C)

5 $ms^{-1}$

Answer 2

The velocity of Ram with respect to Shyam is given by $\vec{v}_{RS} = \vec{v}_R - \vec{v}_S$. Given $\vec{v}_R = -3\hat{i}$ and $\vec{v}_S = -4\hat{j}$, then $\vec{v}_{RS} = -3\hat{i} + 4\hat{j}$. The magnitude of this relative velocity is:

$|\vec{v}_{RS}| = \sqrt{(-3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, ms^{-1}$.