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The height has to change by a factor of 1.
We can obtain the height from which the object falls using the equations of kinematics under gravity. We can see that the object was dropped from a height thus u = 0 m/s.
We can the write;
v= √2gh
h1 = v^2/2g
When the final velocity is doubled, we have;
2v= √2gh
h2 =4v^2/2g
h2 = 2v^2/g
The height changes by;
2v^2/g - v^2/2g = v^2/g
Thus the height has to change by a factor of 1.
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