Answer:
[tex]4.5\ \text{s}[/tex]
Step-by-step explanation:
t = Time taken
u = Initial velocity =17 m/s
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity = 9.81 m/s² = a
[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-17^2}{2\times -9.81}\\\Rightarrow s=14.73\ \text{m}[/tex]
Total height the rock is to fall when it is 8 meters from the ground is [tex]14.73+(31-8)=37.73\ \text{m}[/tex]
[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17}{-9.81}\\\Rightarrow t=1.73\ \text{s}[/tex]
Time taken to reach the maximum height is 1.73 s.
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 37.73=0+\dfrac{1}{2}\times 9.81t^2\\\Rightarrow t=\sqrt{\dfrac{37.76\times 2}{9.81}}\\\Rightarrow t=2.77\ \text{s}[/tex]
Time taken from the maximum height to the point which is 8 m from the ground is 2.77 s.
So, time taken from the moment of the throw to the point 8 m from the ground is [tex]1.73+2.77=4.5\ \text{s}[/tex].
