# An object is thrown vertically from a height of #9 m# at #23 ms^-1#. How long will it take for the object to hit the ground?

##### 1 Answer

Assuming the initial velocity is downward, the object will hit the ground after

#### Explanation:

The question is a little ambiguous: is the object initially thrown upward, downward, horizontally or at an angle? I will assume it is thrown downward, but as a bonus will calculate the time taken if it is thrown upward.

Assuming it is thrown downward, the initial velocity of

Substituting in what we know, we get:

Rearrange to standard form for a quadratic equation:

I won't do it here, but I'd solve this with the quadratic formula, though there are other approaches. The roots are

(as a quick check for sensibleness you could calculate that a stone simply dropped from 9 m would take

(If we assume instead that the stone was thrown upward, we simply give the initial velocity a negative sign, since it is in the opposite direction to the acceleration. Working it through gives