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?

1 Answer
Jan 23, 2016

Answer:

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#