A man falling vertivally by parachute in a steady downpour of rain observes that when his speed is V1 the rain appears to make angle α with the upward vertical.When his speed is V2(V2>V1) the rain appears to make angle ß with the upward vertical.
Show that the rain actually falls at an angle Θ with the vertical given by
(V2-V1)cotΘ=V2cotα-V1cotß.
The velocity of man is "\\vec V_{1}=-V_1\\vec j."
Suppose the relative velocity of the wind is
The velocity of the wind is
The velocity of man is "\\vec V_{2}=-V_2\\vec j."
Suppose the relative velocity of the wind is
The velocity of the wind is
Then
"\\cot(\\Theta)=\\dfrac{-V_2+b\\cos(\\alpha)}{b\\sin(\\beta)}"
"b\\sin(\\beta)\\cot(\\Theta)=-V_2+b\\sin(\\beta)\\cot(\\beta)"
"(V_2-V_1)\\cot(\\Theta)=-V_2((\\cot(\\beta)-\\cot(\\alpha)))"
"+(V_2-V_1)\\cot(\\beta)"
"(V_2-V_1)\\cot(\\Theta)=V_2\\cot(\\alpha)-V_1\\cot(\\beta)"
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