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A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60o with the vertical. The relative velocity of rain with respect to man is:?
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A stationary man observes that the rain is falling vertically downward...
**Answer:**
To solve this problem, we need to analyze the motion of raindrops as observed by the stationary man and the running man separately.
Let's consider the raindrops falling vertically downward as observed by the stationary man. In this case, the velocity of raindrops with respect to the stationary man is simply the vertical velocity component, which we can denote as Vr.
Now, when the man starts running with a velocity of 12 km/h, the raindrops appear to fall at an angle of 60 degrees with the vertical. Let's analyze this situation further.
**Relative Velocity of Raindrops with respect to the Man:**
To find the relative velocity of the raindrops with respect to the running man, we need to consider the vector sum of the man's velocity (Vm) and the raindrops' velocity (Vr).
Let's assume that the raindrops are falling vertically downward in the frame of reference of the stationary man. In this case, the raindrops have a velocity of Vr.
When the man starts running, his velocity is Vm = 12 km/h. This velocity can be broken down into horizontal and vertical components. Since the raindrops are falling at an angle of 60 degrees with the vertical, the horizontal component of the man's velocity does not affect the relative velocity of the raindrops with respect to the man.
Therefore, the relative velocity of the raindrops with respect to the running man can be determined by considering the vertical component of the man's velocity and the vertical component of the raindrops' velocity.
**Using Trigonometry:**
We can use trigonometry to determine the vertical component of the raindrops' velocity and the relative velocity of the raindrops with respect to the man.
Let's denote the magnitude of the relative velocity of the raindrops with respect to the man as Vrel. Using trigonometry, we can relate Vrel, Vm, and Vr as follows:
Vrel/sin(60) = Vm/sin(90)
Vrel/sqrt(3)/2 = 12 km/h
Vrel = 12 km/h * sqrt(3)/2
Vrel = 6 km/h * sqrt(3)
Therefore, the relative velocity of the raindrops with respect to the running man is 6 km/h * sqrt(3) and it makes an angle of 60 degrees with the vertical.
To solve this problem, we need to analyze the motion of raindrops as observed by the stationary man and the running man separately.
Let's consider the raindrops falling vertically downward as observed by the stationary man. In this case, the velocity of raindrops with respect to the stationary man is simply the vertical velocity component, which we can denote as Vr.
Now, when the man starts running with a velocity of 12 km/h, the raindrops appear to fall at an angle of 60 degrees with the vertical. Let's analyze this situation further.
**Relative Velocity of Raindrops with respect to the Man:**
To find the relative velocity of the raindrops with respect to the running man, we need to consider the vector sum of the man's velocity (Vm) and the raindrops' velocity (Vr).
Let's assume that the raindrops are falling vertically downward in the frame of reference of the stationary man. In this case, the raindrops have a velocity of Vr.
When the man starts running, his velocity is Vm = 12 km/h. This velocity can be broken down into horizontal and vertical components. Since the raindrops are falling at an angle of 60 degrees with the vertical, the horizontal component of the man's velocity does not affect the relative velocity of the raindrops with respect to the man.
Therefore, the relative velocity of the raindrops with respect to the running man can be determined by considering the vertical component of the man's velocity and the vertical component of the raindrops' velocity.
**Using Trigonometry:**
We can use trigonometry to determine the vertical component of the raindrops' velocity and the relative velocity of the raindrops with respect to the man.
Let's denote the magnitude of the relative velocity of the raindrops with respect to the man as Vrel. Using trigonometry, we can relate Vrel, Vm, and Vr as follows:
Vrel/sin(60) = Vm/sin(90)
Vrel/sqrt(3)/2 = 12 km/h
Vrel = 12 km/h * sqrt(3)/2
Vrel = 6 km/h * sqrt(3)
Therefore, the relative velocity of the raindrops with respect to the running man is 6 km/h * sqrt(3) and it makes an angle of 60 degrees with the vertical.
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A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60o with the vertical. The relative velocity of rain with respect to man is:?
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A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60o with the vertical. The relative velocity of rain with respect to man is:? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60o with the vertical. The relative velocity of rain with respect to man is:? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60o with the vertical. The relative velocity of rain with respect to man is:?.
A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60o with the vertical. The relative velocity of rain with respect to man is:? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60o with the vertical. The relative velocity of rain with respect to man is:? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60o with the vertical. The relative velocity of rain with respect to man is:?.
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