Question

An object is thrown vertically from a height of `12 m` at `19 ms^-1`. How long will it take for the object to hit the ground?

Answer 1

Assuming the object was thrown downward, the time taken will be `0.55` `s`.

Explanation:

We know:

`u=19` `ms^-1`
`d=12` `m`
`a=9.8` `ms^-2`
`t=?` `s`

(we are choosing downward as the positive direction, since both the initial velocity and the acceleration are in that direction)

Use `d=ut+1/2at^2`

This one is not so easy to rearrange to have `t` as the subject, so let's just substitute in what we know:

`d=ut+1/2at^2 to 12`
`19*t +1/2*9.8*t^2`

Rearrange the quadratic into standard form:

`4.9t^2+19t-12=0`

Solve the quadratic equation using the quadratic formula, or whichever other method you prefer. This yields two roots, but one makes more sense than the other:

`t= -4.4` `s` or `t=0.55` `s`