Q13. A stone is dropped from a height of 5 km. The distance it falls through varies directly with the

Answer:

During the 5th second, the stone travels 36 meters. The correct answer is A.

Step-by-step explanation:

Proportions

Two quantities are considered proportional if one can be derived from the other by multiplying by a constant. If we denote these variables as y and x, it can be expressed as:

y=k.x

There are other forms of proportions where the relationship is non-linear. For example, if y varies with the square of x, we can represent this as:

According to the problem's parameters, the distance a stone drops from a height of 5 km is directly proportional to the square of the time taken during the descent. If d denotes the distance and t indicates time, we have:

To determine the constant k, we apply the provided information: the stone falls d=66 meters in t=4 seconds. By substituting:

Solving this yields:

Using the value of k in the equation completes the model.

Next, we calculate the distance after t=5 seconds:

After 5 seconds, the stone has traveled 100 meters. However, we need the distance for just the 5th second, specifically between 4 and 5 seconds.

We already know the distance at t=4 seconds is 64 meters and at t=5 seconds it's 100 meters:

distance in the 5th second = 100 m - 64 m = 36 m

The stone covers 36 m in the 5th second. Select option A.