Answer:
f = 0.84 or 84%
Step-by-step explanation:
Given:
- Original constant velocity of water v_o = 3.5 m/s
- The original diameter of the hose opening d_o = 1.5 cm
- The total vertical distance y(f) = 1.0 m
- The total range x(f) = 10.0 m
Find:
What fraction of the original area does Isabella has to reduce or pinch so the water can cover the entire range.
Solution:
- We will assume the flow of water as a stream of particles that follow a path of single point.
- Using second kinematic equation in the vertical direction and compute the time it takes the water to reach the ground:
y(t) = y(0) + v_y*t + 0.5*gt^2
Where, y(0) = v_y = 0,
1.0 = 0.5*g*t^2
t = sqrt ( 2*1 / 9.81 )
t = 0.4515 s
- Now we will use the second equation of motion for the x- direction motion:
x(t) = x(0) + v_x*t
Where, x(0) = 0,
10 = 0 + v_x*(0.4515)
v_x = 10 / 0.4515 = 22.1 m/s
- We have calculated the minimum velocity required to reach the range from isabella and ferdinand.
- We will use the continuity equation to compute the area required for the velocity calculated v_x = 22.1 m/s:
A_f*v_x = A_o*v_o
A_f = A_o*v_o / v_x
A_f = pi*0.015^2*3.5 / 4*22.1
A_f = 1.12 * 10^-4 m^2
- The fraction f of the reduction of area is:
f = (A_o - A_f) / A_o
f = (7.068*10^-8 - 1.12*10^-4) / (7.068*10^-8)
f = 0.84 or 84%
