Question

An object is thrown vertically from a height of `2 m` at `15m/s`. How long will it take for the object to hit the ground?

Answer 1

Approximately `1.654` seconds (if I didn't mess up the calculations)

Explanation:

For a distance, `d`, an initial velocity, `v_0`, an acceleration of `a`, and a time of `t`
`color(white)("XXX")d=v_0t+at^2`

In this case
`color(white)("XXX")d=-2 " m"` (2 meters below the height from with it was thrown)
`color(white)("XXX")v_0= 15 " m"/"sec"`
`color(white)("XXX")a=-9.8 " m"/(sec"^2)` (standard gravity assumed)

So we have
#color(white)("XXX")-2.0" m" = 15.0t " m" + (-9.8t^2)" m"

`color(white)("XXX")98t^2-150t-20=0`

Using the quadratic formula:
`color(white)("XXX")t=(150+-sqrt(150^2-4(98)(-20)))/(2(98))`

`color(white)("XXX")t=1.65399color(white)("XX")` or `color(white)("XX")t=-0.12386`

The negative value can be ignored as extraneous.