Question

When you drop a pebble from height H, it reaches the ground with speed V if there is no air resistance. From what height should you drop it so it will reach the ground with three times the speed?

Answer 1

The fall of a pebble is essentially it moving through a distance with a constant acceleration due to gravity.

We have a formula relating velocity to the acceleration of a body and the distance through which it acts.

where, is the final velocity, is the initial velocity, is the acceleration and is the distance through which the acceleration acts.

In our case,

, , and .

Therefore,

in the case of our pebble.

In our second case, we want three times the final velocity of the first case. Lets drop it this time from a height .

Then

Now, we need to find the relation between and .

So we decide the second equation by the first.

From this, we can see that we have to drop the ball from nine times its original height to attain three times the original speed.