A man is running on a horizontal direction on a road at a velocity of 8 km/hr. finds the rain falling in the vertical direction. He increases his speed to 12 Km/hr. & finds that the rain drops make an angle of 30 o with the vertical. Find the velocity and the direction of the rain w.r.t. the road.
Answers
Answered by
146
let the rain drops have a velocity of v kmph and be inclined at an angle A wrt the vertical. So they make an angle 90-A wrt the road.
horizontal component of rain drops = v cosA = 8 kmph. --- (1)
When the person speeds up to 12 kmph, then rain drops fall at an angle of 30 deg. in the opposite direction. Net horizontal component of relative velocity = 12 kmph - 8 kmph = 4 kmph
so tan 30 = 4/(v sin A) => v sin A = 4 √3 kmph ---(2)
so v^2 = 112 => v = 4 √7 kmph
Angle that rain makes with the road
= 90-A = cos⁻¹ (2/√7) = 40.89 deg.
horizontal component of rain drops = v cosA = 8 kmph. --- (1)
When the person speeds up to 12 kmph, then rain drops fall at an angle of 30 deg. in the opposite direction. Net horizontal component of relative velocity = 12 kmph - 8 kmph = 4 kmph
so tan 30 = 4/(v sin A) => v sin A = 4 √3 kmph ---(2)
so v^2 = 112 => v = 4 √7 kmph
Angle that rain makes with the road
= 90-A = cos⁻¹ (2/√7) = 40.89 deg.
Answered by
7
Answer: 4√7 km/h with angle cot-¹ √3/2
Explanation: this question is from concepts of physics by HCV
Attachments:
Similar questions