A person standing on a road has to hold his umbrella at 60degree with the vertical to keep the rain away he thrown the umbrella and start running at 20mpersec he find that the rain drop are hitting his head vertically find the speed of the rain drops with respect to a road and the moving person?

Question

Answer

Analysis:
To solve this problem, we need to consider the relative motion of the raindrops with respect to the person standing on the road. Let's break down the problem into different components.

Component 1: Raindrops falling vertically:
Since the person observes the raindrops falling vertically, it means that their velocity is purely in the vertical direction. Therefore, the vertical component of the velocity of raindrops is equal to zero.

Component 2: Person running at 20 m/s:
The person is running at a speed of 20 m/s. This velocity vector has both horizontal and vertical components. The horizontal component of the velocity remains constant, while the vertical component is zero because the person is running parallel to the ground.

Component 3: Umbrella tilted at 60 degrees:
When the person throws the umbrella and starts running, the umbrella is tilted at an angle of 60 degrees with the vertical. This indicates that the raindrops will follow the path of a projectile under the influence of gravity.

Speed of raindrops with respect to the road:
To find the speed of the raindrops with respect to the road, we need to consider the vector addition of the person's velocity and the raindrops' velocity. Since the raindrops have no horizontal velocity, their speed with respect to the road is equal to the horizontal component of the person's velocity.

Speed of raindrops with respect to the moving person:
To determine the speed of the raindrops with respect to the moving person, we need to calculate the vector difference between the person's velocity and the raindrops' velocity. Since the raindrops have no vertical velocity, their speed with respect to the moving person is equal to the magnitude of the person's velocity vector.

Conclusion:
The speed of the raindrops with respect to the road is equal to the horizontal component of the person's velocity, which is 20 m/s. The speed of the raindrops with respect to the moving person is equal to the magnitude of the person's velocity vector, which is also 20 m/s.

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