Rain is falling vertically downwards with a speed of $30 ext{ m/s}$. A woman rides a bicycle with a speed of $10 ext{

Question

Rain is falling vertically downwards with a speed of $30	ext{ m/s}$. A woman rides a bicycle with a speed of $10	ext{ m/s}$ from north to south. What is the apparent velocity of rain relative to the woman?

Accepted Answer

Let downward be $-\hat{j}$ and south be $-\hat{i}$. Velocity of rain $\vec{v}r = -30\hat{j}$. Velocity of woman $\vec{v}w = -10\hat{i}$. Velocity of rain relative to woman $\vec{v}{rw} = \vec{v}r - \vec{v}w = -30\hat{j} - (-10\hat{i}) = 10\hat{i} - 30\hat{j}$. Magnitude $= \sqrt{10^2 + (-30)^2} = \sqrt{100 + 900} = \sqrt{1000} = 10\sqrt{10}	ext{ m/s}$.

Motion in a Plane

❓ Sibling Questions in this Chapter