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?

1 Answer
Sep 8, 2016

Answer:

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.