A stone is allowed to fall freely from rest. The ratio of the time taken to fall through the first meter and the second metre distance iscorrect answer: √2+1how to solve?

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Answer

Calculation of the time taken by a stone to fall freely through two meters distance

When a stone is allowed to fall freely from rest, it experiences only one force, which is the force of gravity acting downwards. This force causes the stone to accelerate downwards at a constant rate. The acceleration due to gravity is denoted by 'g' and its magnitude is approximately 9.8 m/s².

Calculation of the time taken to fall through one meter distance

The distance travelled by a freely falling stone is given by the formula:

d = ½ gt²

Where d is the distance travelled, g is the acceleration due to gravity and t is the time taken.

When the distance travelled is one meter, the formula becomes:

1 = ½ gt²

Simplifying this equation, we get:

t = √(2/g)

Therefore, the time taken to fall through one meter distance is given by √(2/g).

Calculation of the time taken to fall through two meters distance

Using the formula for distance travelled by a freely falling stone, we can calculate the time taken to fall through two meters distance as follows:

2 = ½ gt²

Simplifying this equation, we get:

t = √(4/g)

Therefore, the time taken to fall through two meters distance is given by √(4/g).

Calculation of the ratio of the time taken to fall through the first and second meter distances

Dividing the time taken to fall through the first meter distance by the time taken to fall through the second meter distance, we get:

√(2/g)/√(4/g)

Simplifying this expression, we get:

√2/2

Therefore, the ratio of the time taken to fall through the first and second meter distances is √2/2.

Conclusion

Thus, we have calculated the time taken by a stone to fall freely through two meters distance and found the ratio of the time taken to fall through the first and second meter distances to be √2/2.

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