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Reika [66]
3 years ago
6

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

Mathematics
2 answers:
Simora [160]3 years ago
8 0
I’m not sure but I think it might be C so sorry if it’s wrong
Colt1911 [192]3 years ago
3 0

Answer:

<em>The stone covers 36 m in the 5th second. Correct choice: A.</em>

Step-by-step explanation:

<u>Proportions</u>

Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:

y=k.x

There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:

y=k.x^2

According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;

d=k.t^2

To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:

64=k.4^2=16k

Solving:

k=64/16=4

Substitute the value of k into the equation to get the complete model.

d=4.t^2

Now we calculate the distance when t=5 seconds:

d=4\cdot 5^2=4\cdot 25=100

The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.

Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:

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

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

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