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When a man moves down the fixed inclined plane with a constant speed 5m/s which makes an angle of 370 with the horizontal, he finds that the rain is falling vertically downward. When he moves up the same inclined plane with the same speed, he finds that the rain makes an angle theta=tan ^ -1 (7/8) with the horizontal. The speed of the rain is? Answer:root(32)

When a man moves down the fixed inclined plane with a constant speed 5m/s which makes an angle of 370 with the horizontal, he finds that the rain is falling vertically downward. When he moves up the same inclined plane with the same speed, he finds that the rain makes an angle theta=tan ^ -1 (7/8) with the horizontal. The speed of the rain is?
 
Answer:root(32)

Grade:11

3 Answers

Venkat
273 Points
5 years ago
Let the velocity of rain be V_r
V_r=a\vec{i}+b\vec{j}
The magnitude of velocity of rain  is  V_r=\sqrt{a^2+b^2}
 
Let  the velocity of man be V_m
 
Now relative velocity is V_{rm}
V_{rm}=V_r-V_m
 
Case (1); When the man goes down the inclined plane,
V_m=-5cos37\vec{i}-5sin37\vec{j}
Here, the vector is in third quadrant. Hence, i and j are negative
 
V_{rm}=V_r-V_m \\V_{rm}=(a-(-5cos37))\vec{i}+(b-(-5sin37))\vec{j}
 
Given that relative velocity is  vertical, V_{rm} is equal to 0\vec{i}. Hence,
0\vec{i}=(a-(-5cos37))\vec{i} \\a=-4
 
Case (2): Man goes up. Hence,
V_m=5cos37\vec{i}+5sin37\vec{j}
Here, the vector is in first quadrant. Hence, i and j are positive.
 
now,
V_{rm}=V_r-V_m \\V_{rm}=(a-5cos37))\vec{i}+(b-5sin37))\vec{j}
 
Take tan of the above vector.
\\tan\theta=\frac{b-5sin37}{a-5cos37} \\ \\tan(tan^{^{-1}}(\frac{7}{8}))=\frac{b-3}{-4-4} \\ \\\frac{7}{8}=\frac{b-3}{-8} \\ \\b=-7+3=-4
 
Velcoity of rain is
\\V_r=\sqrt{a^2+b^2} \\V_r=\sqrt{4^2+(-4)^2} \\V_r=\sqrt{32}
 
 
 
 
Venkat
273 Points
5 years ago
note that there is a small type error in velocity or rain equation. A negative sign is left out for ‘a’.
a= -4
b=-4
V_r=sqrt((-4)^2+(-4)^2) = sqrt(32)
Raj
26 Points
5 years ago
It would be highly helpful if you would have send the diagram too..................................................

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