a person standing on a road has to hold his umbrella at 60 degree vertical to keep the rain away he throws the umbrella and starts running at 20 m/s he finds that rain drops are falling in him vertically. find the speed of the rain drops with respect to
1.the road
2.the moving person
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Bbhdrugdykh
To find the speed of the raindrops with respect to the road and the moving person, we can break down the problem into two parts.
1. Speed of the Raindrops with Respect to the Road:
Since the person standing on the road observes the raindrops falling vertically, we can assume that the vertical velocity of the raindrops is zero with respect to the road. Therefore, the speed of the raindrops with respect to the road is also zero.
2. Speed of the Raindrops with Respect to the Moving Person:
To find the speed of the raindrops with respect to the moving person, we need to consider both the vertical and horizontal components of the raindrops' velocity.
Let's assume that the raindrops have a constant vertical speed "v" and no horizontal velocity with respect to the road. The person standing on the road holds the umbrella at a 60-degree angle to keep the rain away. This means that the vertical component of the raindrops' velocity should be equal to the vertical component of the person's velocity.
The person starts running at a speed of 20 m/s horizontally. Since the raindrops fall vertically (90-degree angle with the road), the vertical component of the raindrops' velocity should also be 20 m/s.
Using basic trigonometry, we can determine the horizontal component of the raindrops' velocity:
cos(60 degrees) = adjacent/hypotenuse
cos(60 degrees) = horizontal velocity/20 m/s
Simplifying, we have:
horizontal velocity = 20 m/s * cos(60 degrees)
horizontal velocity = 20 m/s * 0.5
horizontal velocity = 10 m/s
Therefore, the speed of the raindrops with respect to the moving person is 10 m/s horizontally (in the same direction as the person's motion) and 20 m/s vertically (opposite to the person's motion).