An object is thrown vertically from a height of #9 m# at # 2 m/s#. How long will it take for the object to hit the ground?

1 Answer

Answer:

time #t=1.574623134" "#seconds if thrown upward
time #t=1.166459869" "#seconds if thrown downward

Explanation:

The formula for free falling bodies

#s=v_0*t+1/2*g*t^2#
given #s=9" "#meters
#v_0=2" "#meter/second

There are two solutions for the problem
(1) If the object is thrown vertically upward
#s=v_0*t+1/2*g*t^2#
#-9=(2)*t+1/2(-9.8)*t^2#

#4.9t^2-2t-9=0#

Using quadratic formula

#t=(-(-2)+-sqrt((-2)^2-4(4.9)(-9)))/(2(4.9))#

#t_1=+1.574623134" "#seconds
#t_2=-1.166459869" "#seconds

(2) If the object is thrown vertically downward
#s=v_0*t+1/2*g*t^2#
#-9=(-2)*t+1/2(-9.8)*t^2#

#4.9t^2+2t-9=0#

Using quadratic formula

#t=(-(+2)+-sqrt((+2)^2-4(4.9)(-9)))/(2(4.9))#

#t_1=+1.166459869" "#seconds
#t_2=-1.574623134" "#seconds

God bless....I hope the explanation is useful.