An object is thrown vertically from a height of #6 m# at # 1 m/s#. How long will it take for the object to hit the ground?

1 Answer
Feb 10, 2016

Answer:

#t=1,0087 s#
t=0,872 s#

Explanation:

#"if object moves downward:"#
#h=v_i*t+1/2*g*t^2# ;;#6=1*t+1/2*9,81*t^2#
#6=t+4,905*t^2#
#4,905*t^2+t-6=0#;#ax^2+bx+c=0#
#Delta=sqrt(b^2-4*a*c)# ;#Delta=sqrt(1+4*4,905*6)#
#Delta =sqrt(118,72)#
#Delta=10,896#
#color(red)(t=(-b-Delta)/2*a)" time is not negative " #
#color(green)(t=(-b+Delta)/2*a)#
#t=(-1+10,896)/(2*4,905)#;;#t=(9,896)/(9,81)#
#t=1,0087 s#
#"if object moves upward:"#
#t_u=v_i/g=t_u=1/(9,81)#
#t=0,1019 s" elapsed time while object moves upward"#
#h_u=V_i^2/(2*g)=1/(19,62)=0,051 m " height from starting point"#
#h=6+0,051=6,051 m " height to ground"#
#h=1/2 *g*t^2 " freely falling"#
#6,051=1/2*9,81*t^2 ; t=sqrt((2*6,051)/(9,81)) t=0,872 s#