Question

69. Rain is falling vertically with a speed of 20 ms relative to air. A person is running in the rain with a velocity
of 5 ms and a wind is also blowing with a speed of 15 ms (both towards east). Find the angle with the
vertical at which the person should hold his umbrella so that he may not get drenched.
​

Answer 1

Dear Student,

◆ Answer -

θ = 26.57°

● Explanation -

Let's consider i' as unit vector along horozontal and j' be unit vector along vertical.

So given is -

vm = 5i m/s

vw = 15i m/s

vr = 20j m/s

So now, velocity of man w.r.t. man with wind blowing is -

v = vr - vm + vw

v = 20j - 5i + 15i

v = 20j + 10i m/s

Let θ be angle of umbrella with the vertical.

tanθ = vx/vy

tanθ = 10/20

θ = tan⁻¹(1/2)

θ = 26.57°

Therefore, umbrella should make a angle of 26.57°.

Thanks dear...

Answer 2

Let East be along +ve x-axis and vertically up be along +ve y-axis

⇒ Speed of man=  

V  

m

​  

 

​  

=5  

i

^

 

⇒ Speed of wind=  

V  

w

​  

 

​  

=15  

i

^

 

⇒ Speed of  rain relative to wind=  

V  

r

​  

 

​  

−  

V  

w

​  

 

​  

=−20  

j

^

​  

 

⇒ Speed of rain=  

V  

r

​  

 

​  

=15  

i

^

−20  

j

^

​  

 

Now, speed of man relative to  rain=  

V  

m

​  

 

​  

−  

V  

r

​  

 

​  

=5  

i

−(15  

i

^

−20  

j

^

​  

)=−10  

i

^

+20  

j

^

​  

 

Tan of angle from vertical at which the person should hold his umbrella=10/20=1/2