Question

A man is walking due east at a rate of $5km/h$ and the rain appears to be falling vertically with a speed of $12km/h$. Calculate the true speed of rain.

• A. $\sqrt{1}3km/h$
  
• B. $12km/h$
  
• C. $5km/h$
  
• D. $13km/h$

Answer 1

The correct option is D $13km/h$

$V_{Rain,Person}=V_{Rain}-V_{Person}=-12\hat{j}$ (vertically down)

Thus, $V_{Rain}-\left(5\hat{i}\right)=-12\hat{j}($take east as $\hat{i})$

or, $V_{Rain}=5\hat{i}-12\hat{j}$

Thus, magnitude $=13km/hr$