Relative Motion

Question

Rain falls vertically at 6 m/s. Person runs east at 8 m/s. Relative velocity components of rain w.r.t runner are:

RankGuru · Accepted Answer

Let the vertical (down) direction be $-\hat{j}$ and east be $+\hat{i}$.
- Velocity of rain $\vec{v}_r = -6 \hat{j} 	ext{ m/s}$
- Velocity of person $\vec{v}_p = 8 \hat{i} 	ext{ m/s}$
Relative velocity of rain with respect to person is:
$\vec{v}_{rp} = \vec{v}_r - \vec{v}_p = -6 \hat{j} - 8 \hat{i} 	ext{ m/s}$.
The components are:
- Vertical component: $6 	ext{ m/s}$
- Horizontal component: $8 	ext{ m/s}$
(Magnitude would be $\sqrt{6^2 + 8^2} = 10 	ext{ m/s}$ at an angle).

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