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A man running on A horizontal road at 8km/hr finds the rain falling vertically. If he increases its speed to 12km/hr and finds that the drops makes an angle 30degree with vertical. Find speed and direction of rain with respect to road?
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A man running on A horizontal road at 8km/hr finds the rain falling ve...
Given information:
A man is running on a horizontal road at a speed of 8 km/hr. Initially, he observes the rain falling vertically. When he increases his speed to 12 km/hr, he observes that the raindrops make an angle of 30 degrees with the vertical.
To find:
The speed and direction of rain with respect to the road.
Approach:
To find the speed and direction of rain with respect to the road, we need to consider the relative motion of the man and the rain.
1. Initial observation:
- When the man is running at a speed of 8 km/hr, he observes the rain falling vertically.
- This means that the man and the raindrops are moving in the same direction with the same speed.
- So, the speed of raindrops with respect to the man is 0 km/hr.
2. Observation at increased speed:
- When the man increases his speed to 12 km/hr, he observes the raindrops making an angle of 30 degrees with the vertical.
- This means that the man and the raindrops are no longer moving in the same direction with the same speed.
- The raindrops appear to be coming at an angle to the vertical, indicating that there is a relative motion between the man and the raindrops.
- We need to find the speed and direction of this relative motion.
3. Using trigonometry:
- Let's assume the speed of rain with respect to the road is 'v' km/hr. This is the quantity we need to find.
- The speed of the man with respect to the road is given as 8 km/hr.
- We can use the concept of trigonometry to relate the speeds of the man, rain, and the relative speed.
- In a right-angled triangle formed by the vertical direction, the direction of rain, and the relative direction, we can use the sine function to relate the angles and speeds.
- We have sin(30 degrees) = (v - 8) / 12, as the component of rain's speed perpendicular to the road is (v - 8).
- Solving this equation, we can find the value of 'v'.
Calculation:
sin(30 degrees) = (v - 8) / 12
1/2 = (v - 8) / 12
12/2 = v - 8
6 + 8 = v
v = 14 km/hr
Answer:
The speed of rain with respect to the road is 14 km/hr. The rain is coming from a direction inclined at an angle of 30 degrees to the vertical.
A man is running on a horizontal road at a speed of 8 km/hr. Initially, he observes the rain falling vertically. When he increases his speed to 12 km/hr, he observes that the raindrops make an angle of 30 degrees with the vertical.
To find:
The speed and direction of rain with respect to the road.
Approach:
To find the speed and direction of rain with respect to the road, we need to consider the relative motion of the man and the rain.
1. Initial observation:
- When the man is running at a speed of 8 km/hr, he observes the rain falling vertically.
- This means that the man and the raindrops are moving in the same direction with the same speed.
- So, the speed of raindrops with respect to the man is 0 km/hr.
2. Observation at increased speed:
- When the man increases his speed to 12 km/hr, he observes the raindrops making an angle of 30 degrees with the vertical.
- This means that the man and the raindrops are no longer moving in the same direction with the same speed.
- The raindrops appear to be coming at an angle to the vertical, indicating that there is a relative motion between the man and the raindrops.
- We need to find the speed and direction of this relative motion.
3. Using trigonometry:
- Let's assume the speed of rain with respect to the road is 'v' km/hr. This is the quantity we need to find.
- The speed of the man with respect to the road is given as 8 km/hr.
- We can use the concept of trigonometry to relate the speeds of the man, rain, and the relative speed.
- In a right-angled triangle formed by the vertical direction, the direction of rain, and the relative direction, we can use the sine function to relate the angles and speeds.
- We have sin(30 degrees) = (v - 8) / 12, as the component of rain's speed perpendicular to the road is (v - 8).
- Solving this equation, we can find the value of 'v'.
Calculation:
sin(30 degrees) = (v - 8) / 12
1/2 = (v - 8) / 12
12/2 = v - 8
6 + 8 = v
v = 14 km/hr
Answer:
The speed of rain with respect to the road is 14 km/hr. The rain is coming from a direction inclined at an angle of 30 degrees to the vertical.
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A man running on A horizontal road at 8km/hr finds the rain falling ve...
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A man running on A horizontal road at 8km/hr finds the rain falling vertically. If he increases its speed to 12km/hr and finds that the drops makes an angle 30degree with vertical. Find speed and direction of rain with respect to road? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A man running on A horizontal road at 8km/hr finds the rain falling vertically. If he increases its speed to 12km/hr and finds that the drops makes an angle 30degree with vertical. Find speed and direction of rain with respect to road? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man running on A horizontal road at 8km/hr finds the rain falling vertically. If he increases its speed to 12km/hr and finds that the drops makes an angle 30degree with vertical. Find speed and direction of rain with respect to road?.
A man running on A horizontal road at 8km/hr finds the rain falling vertically. If he increases its speed to 12km/hr and finds that the drops makes an angle 30degree with vertical. Find speed and direction of rain with respect to road? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A man running on A horizontal road at 8km/hr finds the rain falling vertically. If he increases its speed to 12km/hr and finds that the drops makes an angle 30degree with vertical. Find speed and direction of rain with respect to road? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man running on A horizontal road at 8km/hr finds the rain falling vertically. If he increases its speed to 12km/hr and finds that the drops makes an angle 30degree with vertical. Find speed and direction of rain with respect to road?.
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