A stone is projected upwards from the top of abuilding with some initial speed and reaches theground in 5sec. Now it is allowed to fall with thesame initial speed downwards and reaches theground in 3 sec. If the stone is allowed to fall freelyunder gravity from the same point, it will reach the ground ina)4 sb)2 sc)15 sd)8 sCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given data:
- A stone is projected upwards from the top of a building with some initial speed and reaches the ground in 5 sec.
- It is allowed to fall with the same initial speed downwards and reaches the ground in 3 sec.

To find:
- Time taken by the stone to fall freely under gravity from the same point.

Solution:
Let's assume that the height of the building from which the stone is projected is 'h' and the initial velocity with which the stone is projected upwards is 'u'. Also, let's assume that the acceleration due to gravity is 'g'.

First case - Stone is projected upwards:
Using the equation of motion:
h = ut - 1/2 * g * t^2

Substituting the given values:
h = u * 5 - 1/2 * g * 5^2

Second case - Stone is allowed to fall downwards:
Using the same equation of motion:
h = 1/2 * g * t^2

Substituting the given values:
h = 1/2 * g * 3^2

Now, let's equate both the equations to find the value of 'u':
u * 5 - 1/2 * g * 5^2 = 1/2 * g * 3^2

Simplifying the above equation:
u = (16/5) * g

Third case - Stone falls freely under gravity:
Using the same equation of motion:
h = 1/2 * g * t^2

Substituting the value of 'h' from the first case:
u * t - 1/2 * g * t^2 = 1/2 * g * t^2

Simplifying the above equation:
t = 2u/g

Substituting the value of 'u':
t = 2 * (16/5) * g / g

Simplifying further:
t = 32/5 sec

Therefore, the time taken by the stone to fall freely under gravity from the same point is 32/5 sec or 6.4 sec (approx).

Hence, the correct answer is option 'C'.

Answer

Use formula √ t1×t2. u will get the answer..

Answer

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