An object of unknown mass is initially at rest and dropped from a height h. It reaches the ground with a velocity v1 . The same object is then raised again to the same height h but this time is thrown downward with velocity v1 . It now reaches the ground with a new velocity v2 . How is v2 related to v1 ?

Explanation:

The velocity v₁ can be calculated with the kinematic formula:

Since the object is initially at rest, v₁ becomes:

Where g is the acceleration due to gravity. Now, the velocity v₂ can be calculated with the same formula, but now the initial velocity is v₁:

Substituting v₁ in this expression and solving for v₂, we get:

Now, dividing v₂ over v₁, we get the expression:

It means that v₂ is √2 times v₁.

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