Question

When it is raining vertically down,to a man walking on road the velocity of rain appears to be 1.5 times his velocity.To protect himself from rain he should hold the umbrella at an angle theta to vertical. Then tan theta=

Answer 1

The value of $\bold{\tan \theta = 0.89}$.

Explanation:

1. Velocity of man = U

2. Velocity of rain with respect to man $V_{R}= 1.5U$   ...1)

3. Velocity of rain in vertical downward = V  

From figure velocity of rain from Pythagoras  

   $V=\sqrt{(V_{R}^{2}-U^{2})}$      ...2)

5. $V=\sqrt{((1.5U)^{2}-U^{2})}$

  Then

  V = 1.12 U = Velocity of rain       ...3)

6. Now from figure

   $\tan \theta =\frac{U}{V}$

  from equation 3)

   $\tan \theta =\frac{U}{1.12}$

 So

   $\tan \theta =0.89$