the distance covered by a falling ball varies as the square of the time taken.if a ball falls through 1800m in 15seconds,calculate the distance when the time taken is 15seconds and the time taken for is distance of 648m.?
(d/1800)=(t/15)^2
648/1800=t^2/225
t= sqrt(225*648/18OO)
That is the time to fall 648 meters.
The distance taken in 15 seconds is 1800m, that was given.
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To find the relationship between distance and time, we know that the distance covered by a falling ball varies as the square of the time taken. So, we can write the equation as follows:
Distance = k * time^2
where k is a constant that we need to find.
Given that the ball falls through 1800m in 15 seconds, we can substitute these values into the equation:
1800 = k * (15)^2
Simplifying the equation, we have:
1800 = k * 225
Solving for the constant k, we divide both sides by 225:
k = 1800 / 225
k = 8
Now that we have the constant 'k', we can use it to find the distance when the time is 15 seconds, and also the time when the distance is 648m.
For distance of 648m, let's find the time taken:
648 = 8 * t^2
Simplifying the equation, we have:
648 = 8t^2
Dividing both sides by 8:
t^2 = 81
Taking the square root of both sides:
t = √81
t = 9 seconds
Therefore, the time taken for a distance of 648m is 9 seconds.
Now, let's find the distance when the time taken is 15 seconds:
Distance = 8 * (15)^2
Distance = 8 * 225
Distance = 1800m
Therefore, when the time taken is 15 seconds, the distance covered by the falling ball is 1800m.
To solve this problem, we can use the given information that the distance covered by a falling ball varies as the square of the time taken.
Let's break down the problem and solve it step by step.
Step 1: Identify the relationship between distance and time.
According to the problem, the distance covered varies as the square of the time taken. This means that the distance (d) is related to the square of the time taken (t^2) through a constant factor.
Step 2: Find the constant factor.
Given that the ball falls through 1800m in 15 seconds, we can use this information to find the constant factor. We can set up an equation using the given information:
1800 = k * (15^2)
Solving for k:
1800 = k * 225
k = 1800 / 225
k = 8
The constant factor (k) is 8.
Step 3: Calculate the distance when the time taken is 15 seconds.
In this step, we need to find the distance (d) when the time taken (t) is 15 seconds. We can use the constant factor (k) and the equation we found earlier:
d = k * (t^2)
d = 8 * (15^2)
d = 8 * 225
d = 1800
So, when the time taken is 15 seconds, the distance covered is 1800m.
Step 4: Calculate the time taken for a distance of 648m.
To find the time taken for a distance of 648m, we can rearrange the equation used earlier:
d = k * (t^2)
Rearranging for t:
t^2 = d / k
t^2 = 648 / 8
t^2 = 81
t = √81
t = 9
So, the time taken for a distance of 648m is 9 seconds.
In conclusion, when the time taken is 15 seconds, the distance covered is 1800m. And when the distance covered is 648m, the time taken is 9 seconds.