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A stationary man observes that the rain strikes him at an angle of 60∘ to the horizontal. When he begins to move with the velocity of 25m/s then the drops appear to strike him at an angle 30∘ from horizontal. The velocity of the rain drops is :

(Explain with diagram)

Asked by shubhkansal75 23rd November 2022, 9:48 PM
Answered by Expert
Answer:
When the man is at rest , direction of rain makes angle 60o with horizontal.
 
Hence relative speed of rain with respect to man, vrel = ( v cos60) begin mathsize 14px style i with hat on top end style  + ( v sin60) begin mathsize 14px style j with hat on top end style
vrel = v [ ( 1/2 ) begin mathsize 14px style i with hat on top end style + ( √3/2) begin mathsize 14px style j with hat on top end style ]
when the man walks with speed 25 m/s , then relative velocity of rain
 
v'rel =  [ v ( 1/2 ) + 25 ] begin mathsize 14px style i with hat on top end style + [ v ( √3 /2) ] begin mathsize 14px style j with hat on top end style
If the direction of rain makes angle 30o with horizontal when the man walks at a velocity 25 m/s ,
 
then we have
 
begin mathsize 14px style fraction numerator v space begin display style fraction numerator square root of 3 over denominator 2 end fraction end style over denominator begin display style v over 2 end style plus 25 end fraction equals tan 30 space end style
 
 
begin mathsize 14px style fraction numerator v space begin display style fraction numerator square root of 3 over denominator 2 end fraction end style over denominator begin display style v over 2 end style plus 25 end fraction equals fraction numerator 1 over denominator square root of 3 end fraction end style
 
By solving above expression, we get magnitude of velocity of rain , v = 25 m/s
Answered by Expert 24th November 2022, 12:01 AM
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