Answer:
H = 171.90 m
Explanation:
given data
distance = 53.2 m
height = H
to find out
height H
solution
we know height is here H = [tex]\frac{1}{2} gt^2[/tex] ......................1
here t is time and a is acceleration
so
we find t first
we know during time (t -1) s , it fall distance (H - 53.2) m
so equation of distance
[tex]H - 53.2 = \frac{1}{2} g (t-1)^2[/tex]
[tex]H - 53.2 = \frac{1}{2} g (t^2-2t+1)[/tex]
[tex]H - 53.2 = \frac{1}{2} gt^2-gt+\frac{1}{2} g[/tex] ................2
now subtract equation 2 from equation 1 so we get
[tex]H - (H - 53.2) =\frac{1}{2} gt^2- (\frac{1}{2} gt^2-gt+\frac{1}{2} g)[/tex]
53.2 = gt - [tex]\frac{1}{2} g [/tex]
53.2 = 9.81 t - [tex]\frac{1}{2} 9.8 [/tex]
t = 5.92 s
so from equation 1
H = [tex]\frac{1}{2} (9.81)5.92^2[/tex]
H = 171.90 m
