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A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth’s surface will be
  • a)
  • b)
    1 : 2
  • c)
    1 : 1
  • d)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A man standing on the roof of a house of height h throws one particle ...
Particle 1 (Thrown Vertically Downward):
Initial velocity (u) is downward.
Final velocity is affected by gravity. Using the equation of motion:
Particle 2 (Thrown Horizontally):
Horizontal velocity remains constant (u).
Vertical velocity due to free fall can be calculated as:
The resultant velocity (v2) at the Earth's surface is given by combining the horizontal and vertical velocities using the Pythagorean theorem:
Velocity Ratio:
The magnitude of both velocities is the same:

Thus, the ratio of their velocities is: 1 : 1
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Community Answer
A man standing on the roof of a house of height h throws one particle ...
According to Question, 
Both particles are thrown with same velocity for top of roof. 
As man detaches (leave) it from hand it has initial velocity =0 m/s. (for both particles)
Then, it is under the influence of gravity  with initial having only acceleration = gravity(g).
From, top to bottom(before touch on ground) it has increasing  velocity as body is accelerating under gravity.
Hence, ratio of initial velocity is 1:1.
                 Therefore,  velocity ratio when they reach earths surface will be 1:1.
Both the particles  are depending upon same factors and under same influence.
                                   ANSWER = (C) 1:1

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