Time taken to cover a height H in 5 seconds
- When a particle falls from rest under gravity, it undergoes free fall motion.
- The distance covered by the particle in free fall motion can be calculated using the equation:
- h = (1/2)gt^2
- where h is the distance covered, g is the acceleration due to gravity, and t is the time taken.
- In this case, the distance covered is H and the time taken is 5 seconds. So we have the equation:
- H = (1/2)g(5)^2
- Solving this equation will give us the value of g.

Time taken to cover the next distance H
- Once we have calculated the value of g, we can use it to find the time taken to cover the next distance H.
- The equation for the distance covered in free fall motion is:
- h = (1/2)gt^2
- Rearranging this equation, we get:
- t = √(2h/g)
- Substituting the value of h as H, we get:
- t = √(2H/g)
- Plugging in the value of g that we calculated earlier, we can find the time taken to cover the next distance H.

Explanation
- When a particle falls from rest under gravity, it accelerates due to the gravitational force.
- The acceleration due to gravity is constant and is approximately 9.8 m/s^2.
- The distance covered by the particle in free fall motion can be calculated using the equation h = (1/2)gt^2.
- In this case, we are given that the particle covers a height H in 5 seconds.
- By substituting the given values into the equation, we can solve for g.
- Once we have the value of g, we can use it to find the time taken to cover the next distance H using the equation t = √(2H/g).
- This equation gives us the time taken to cover the next distance H when the particle continues falling under gravity.