1.

To a man walking at the rate of 3 km/h the rain appears to fall vertically. When he increases his speed to 6 km/h it appears to meet at the angle of 45° with the vertical. Find the speed of rain.​

Answer»

Answer:

Explanation:

To man walking a the rate of 3km/h the RAIN appears to fall vertically

When he increases his speed to  

=6km/h it appears to meet him at an angle of 45° with verticl.

Find the velocity the rain.

Solution  

Let  

i

^

 and  

j

^

​  

 be unit vector in horizontal and vertical respectively

Let, velocity of rain v  

r

​  

=a  

i

^

+b  

j

^

​  

 

Speed off the rain=  

a  

2

+b  

2

 

​  

 

CASE 1

When the RELATIVE velocity of rain with respect to man is vertical

v  

rms

​  

=  

v  

r

​  

 

​  

−  

v  

m

​  

 

​  

 

v  

m

​  

=3  

i

^

 

v  

rms

​  

=(a−3)  

i

^

+b  

j

^

​  

 

SINCE v  

rms

​  

 is vertical

a+3=0⇒a=3

Case 2

When relative velocity is at 45°

m

=6  

i

^

 

v  

rms

​  

=(a−6)  

i

^

+b  

j

^

​  

 

=3  

i

^

+b  

j

^

​  

 

And since tanθ=  

−3

b

​  

 

tan45°=1

∣b∣=3

Therefore speed=  

3  

3

+3  

2

 

​  

 

=3  

2

​



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