Given,
Lia dropped a coin from a certain height above the ground. She measured and represented its displacements x1, x2, and x3 in the first, second, and third seconds of its fall.
To find
The ratio of x1, x2, and x3
Explanation
By equation of kinematics we have,
[tex]s=ut+\frac{1}{2}at^2[/tex]Considering initial velocity to be zero we get,
[tex]s=\frac{1}{2}at^2[/tex]where s is the distance travelled.
With acceleration due to gravity being constant we have,
[tex]s\propto t^2[/tex]So the ratio of the distances is
[tex]x1\colon x2\colon x3=1^2\colon2^2;3^2=1\colon4\colon9[/tex]Conclusion:
The required ratio is
[tex]1\colon4\colon9[/tex]