Astudent drops a rock from rest at a distance h above the ground such that the rock hits the ground at time t0. at what distance above the ground should the rock be dropped such that it hits the ground at a time 2t0 after it is released from rest?

4h

Step-by-step explanation:

This is a classic "free fall" problem. The following equations describe the motion of a free falling mass:

where is the initial position of the mass, its initial speed and is the acceleration due to gravity.

In this case, and

Replacing in the above mentioned equations we obtain:

At we know that

So

Now lets find the distance the rock should be dropped from such that it hits the ground () at

Here we have the answer.