Answer:
3.04 m
Explanation:
20 mm = 0.02 m
10 mm = 0.01 m
When the water escape from the hose opening with a velocity v to rise up to a height of 0.19m, its potential energy is converted from kinetic energy:
[tex]E_p = E_k[/tex]
[tex]mgh = mv^2/2[/tex]
where m is the mass and h is the vertical distance traveled, and g = 9.81m/s2 is the gravitational acceleration
We can divide both sides by m and get:
[tex]gh = v^2/2[/tex]
[tex]h = v^2/(2g)[/tex] (1)
When you cover part of the hose and reduce the cross sectional area, water velocity increases:
[tex]A_1v_1 = A_2v_2[/tex]
[tex]v_2 = v_1\frac{A_1}{A_2}[/tex]
As the area of the circular opening is:
[tex]A = \pi d^2/4[/tex]
where d is the diameter
[tex]v_2 = v_1\frac{\pi d_1^2/4}{\pi d_2^2 /4} = v_1(d_1/d_2)^2 = v_1(0.02 / 0.01)^2 = 4 v_1[/tex]
[tex]v_2^2 = (4v_1)^2 = 16v_1^2[/tex]
[tex]v_2^2/v_1^2 = 16[/tex]
From equation (1) we have the following ratio
[tex]\frac{h_2}{h_1} = \frac{v_2^2/2g}{v_1^2/2g} = v_2^2 / v_1^2 = 16[/tex]
[tex]h_2 = 16h_1 = 16*0.19 = 3.04 m[/tex]
