A stone falls freely from rest from height h and it travels a distance of 9h/25 in the last second then the find value of h , plz solve this question btw its answer is 122.5m

Question

A stone falls freely from rest from height h and it travels a distance of 9h/25 in the last second then the find value of h  , plz solve this question btw its answer is 122.5m

Answer

Problem Statement

A stone falls freely from rest from height h and it travels a distance of 9h/25 in the last second then the find value of h.

Solution

Step 1: Understanding the problem

Let's understand the problem statement. A stone is falling freely from rest from a height h. It travels a distance of 9h/25 in the last second. We need to find the value of h.

Step 2: Free fall equation

When an object falls freely under the influence of gravity, it follows the laws of motion given by the free fall equation:

h = ut + 1/2gt^2

where h is the height of the object at time t, u is the initial velocity of the object (which is zero in this case), g is the acceleration due to gravity, and t is the time elapsed.

Step 3: Finding the time taken

Let's assume that the total time taken by the stone to fall from height h is t seconds. Then, we can write:

h = 1/2gt^2

or

t = sqrt(2h/g)

Step 4: Finding the velocity at the end of the first second

During the first second of the fall, the stone travels a distance given by:

s = 1/2gt^2 = 1/2g

At the end of the first second, the velocity of the stone can be found using the equation:

v = u + gt

where u is the initial velocity (which is zero) and t is the time elapsed (which is one second). Therefore, we have:

v = gt

Step 5: Finding the distance traveled in the last second

We are given that the stone travels a distance of 9h/25 in the last second. Therefore, we can write:

9h/25 = v + 1/2g

where v is the velocity of the stone at the end of the first second (which we have just calculated) and g is the acceleration due to gravity.

Step 6: Solving for h

Let's substitute the value of t from step 4 in the equation for v:

v = gt = g*sqrt(2h/g) = sqrt(2gh)

Substituting this value of v in the equation from step 5, we get:

9h/25 = sqrt(2gh) + 1/2g

Squaring both sides of the equation, we get:

(9h/25 - 1/2g)^2 = 2gh

Expanding and simplifying the equation, we get:

81h^2/625 - 9hg/25 + g^2/4 = 2gh

Answer

H = 1/2 gt^2

Snth =u+ a/2(2n-1)

9h/25 =1/2g(2t-1)

Solving t = 5 s h = 125 m

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