Answer:
[tex]h=7.15cm[/tex]
Explanation:
From kinematics, if the initial velocity of the water coming out of the tank is [tex]v[/tex], then its horizontal range is given by
[tex]d= v\sqrt{\dfrac{2y}{g} }[/tex]
where [tex]y[/tex] is the vertical distance to the hole from the ground, and [tex]g[/tex] is the acceleration due to gravity.
And according to Torricelli's Theorem, the velocity [tex]v[/tex] of water coming out of the hole is
[tex]v=\sqrt{2gh}[/tex]
where [tex]h[/tex] is the distance from the top of the tank as shown in the figure.
We use the horizontal range equation to find the velocity [tex]v[/tex] of water coming out of the hole:
[tex]d= v\sqrt{\dfrac{2y}{g} }[/tex]
[tex]v=d*\sqrt{\dfrac{g}{2y} }[/tex]
and since [tex]d=0.633m[/tex], and [tex]y=1.4m[/tex],
[tex]v=(0.633m)*\sqrt{\dfrac{9.8m/s^2}{2(1.4m)} }[/tex]
[tex]\boxed{v=1.184m/s}[/tex]
Now, we are in position to use Torricelli's theorem to find the height [tex]h[/tex]:
[tex]v=\sqrt{2gh}[/tex]
[tex]h=\dfrac{v^2}{2g}[/tex]
putting in [tex]v=1.184m/s[/tex] we get:
[tex]h=\dfrac{(1.184m/s)^2}{2*9.8m/s^2}[/tex]
[tex]h=0.0715m[/tex]
in centimeters this is
[tex]\boxed{ h=7.15cm.}[/tex]
