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A boy running on a horizontal road at 8 km/h finds the rain falling vertically. He increases his speed to 12 km/h and finds that the drops makes 30° with the vertical. The speed of rain with respect to the road is
  • a)
    4√7 km/h
  • b)
    9√7 km/h
  • c)
    12√7 km/h
  • d)
    15√7 km/h
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A boy running on a horizontal road at 8 km/h finds the rain falling ve...
Degrees with the horizontal. Find the speed and direction of the rain.

Let v be the velocity of rain with respect to the ground and θ be the angle it makes with the horizontal.

When the boy runs at 8 km/h, his velocity with respect to the ground is 8 km/h horizontally. Therefore, the rain appears to be falling vertically, i.e. θ = 0.

When the boy runs at 12 km/h, his velocity with respect to the ground is 12 km/h horizontally. Let u be the velocity of the rain with respect to the boy. Then, the velocity of the rain with respect to the ground is v = u + 12 km/h horizontally.

Using trigonometry, we can write:

tan(30°) = v/u

Substituting v = u + 12 km/h and θ = 30°, we get:

tan(30°) = (u + 12 km/h)/u

Simplifying this equation, we get:

u = 12/√3 km/h = 6√3 km/h

Substituting u in v = u + 12 km/h, we get:

v = 18/√3 km/h = 6√3 * √3/3 km/h

Therefore, the speed of the rain is 6 km/h and the angle it makes with the horizontal is 60° (since tan(60°) = √3).
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A boy running on a horizontal road at 8 km/h finds the rain falling vertically. He increases his speed to 12 km/h and finds that the drops makes 30° with the vertical. The speed of rain with respect to the road isa)4√7 km/hb)9√7 km/hc)12√7 km/hd)15√7 km/hCorrect answer is option 'A'. Can you explain this answer?
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A boy running on a horizontal road at 8 km/h finds the rain falling vertically. He increases his speed to 12 km/h and finds that the drops makes 30° with the vertical. The speed of rain with respect to the road isa)4√7 km/hb)9√7 km/hc)12√7 km/hd)15√7 km/hCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A boy running on a horizontal road at 8 km/h finds the rain falling vertically. He increases his speed to 12 km/h and finds that the drops makes 30° with the vertical. The speed of rain with respect to the road isa)4√7 km/hb)9√7 km/hc)12√7 km/hd)15√7 km/hCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy running on a horizontal road at 8 km/h finds the rain falling vertically. He increases his speed to 12 km/h and finds that the drops makes 30° with the vertical. The speed of rain with respect to the road isa)4√7 km/hb)9√7 km/hc)12√7 km/hd)15√7 km/hCorrect answer is option 'A'. Can you explain this answer?.
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