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.solve using variation
Variation?
15 sec = 1800m
15/1800 = x/648
Solve for x.
pls finish the answer! Very urgent
To solve this problem using variation, we can express the relationship between distance covered (d) and time taken (t) as:
d = k * t^2
where k is the constant of variation.
Given that a ball falls through 1800m in 15 seconds, we can substitute these values into the equation to solve for k:
1800 = k * 15^2
1800 = k * 225
k = 1800 / 225
k = 8
Now that we have the value of k, we can calculate the distance when the time taken is 15 seconds:
d = 8 * 15^2
d = 8 * 225
d = 1800m
So, when the time taken is 15 seconds, the distance covered by the ball is 1800m.
To find the time taken for a distance of 648m, we can rearrange the equation:
d = k * t^2
648 = 8 * t^2
t^2 = 648 / 8
t^2 = 81
t = √81
t = 9 seconds
Therefore, the time taken for a distance of 648m is 9 seconds.
To solve this problem using variation, we need to first understand the relationship between the distance covered by a falling ball and the time taken.
We are given that the distance covered by the ball varies as the square of the time taken. This can be expressed as:
Distance = k * (Time^2)
Where 'k' is a constant of variation. We can find the value of 'k' using the given information.
Given: Distance = 1800m, Time = 15s
Plugging in these values into the equation:
1800 = k * (15^2)
1800 = 225k
Dividing both sides of the equation by 225:
k = 1800 / 225
k = 8
Now with the value of 'k', we can use it to calculate the distance for different time intervals.
1) To find the distance when the time taken is 15 seconds:
Time = 15s
Distance = k * (Time^2)
Distance = 8 * (15^2)
Distance = 8 * 225
Distance = 1800m
Therefore, the distance covered when the time taken is 15 seconds is 1800 meters.
2) To find the time taken for a distance of 648 meters:
Distance = 648m
Using the same equation, we can solve for 'Time':
Distance = k * (Time^2)
648 = 8 * (Time^2)
Dividing both sides of the equation by 8:
81 = Time^2
Taking the square root of both sides:
Time = √81
Time = 9
Therefore, the time taken for a distance of 648 meters is 9 seconds.