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From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:
  • a)
    2gH = n 2 u2
  • b)
    gH = ( n- 2 )2u 2
  • c)
    2gH = nu 2 n- 2
  • d)
    gH = ( n- 2)u 2
Correct answer is option 'C'. Can you explain this answer?
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From a tower of height H, a particle is thrown vertically upwards with...
Ans.

Option (c)

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From a tower of height H, a particle is thrown vertically upwards with...


Concept:
When a particle is thrown vertically upwards, we can analyze the motion using the equations of motion. The time taken by the particle to hit the ground is the total time taken for the upward motion and the downward motion. The time taken to reach the highest point is half of the total time of flight.

Solution:

- Given:
- Initial height of the tower, H
- Initial speed of the particle, u
- Time taken to reach the ground, T
- Time taken to reach the highest point, T/2
- Acceleration due to gravity, g

- Using the equations of motion:
- Time taken to reach the highest point: T/2 = u/g
- Time taken to reach the ground: T = 2u/g

- Given relation:
- T = n(T/2)
- 2u/g = n(u/g)
- 2 = n

- Substitute the value of n in terms of given relation:
- 2 = n
- n = 2

- Substitute the value of n in the equation of motion:
- T = 2u/g
- H = ut - (1/2)gt^2
- H = 2u(2u/g) - (1/2)g(2u/g)^2
- 2gH = 4u^2 - 2u^2
- 2gH = 2u^2
- 2gH = nu^2 (n - 2)

Therefore, the relation between H, u, and n is 2gH = nu^2(n - 2), which is option 'C'.
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From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:a)2gH = n 2 u2b)gH = ( n- 2 )2u 2c)2gH = nu 2 n- 2d)gH = ( n- 2)u 2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:a)2gH = n 2 u2b)gH = ( n- 2 )2u 2c)2gH = nu 2 n- 2d)gH = ( n- 2)u 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:a)2gH = n 2 u2b)gH = ( n- 2 )2u 2c)2gH = nu 2 n- 2d)gH = ( n- 2)u 2Correct answer is option 'C'. Can you explain this answer?.
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