A cowboy at a dude ranch fills a horse trough that is 1.5 m long, 60 cm wide, and 40 cm deep. He uses a 2.0-cm-diameter hose fromwhich water emerges at 1.5 m/s How long does it take him to fillthe trough?

It will take him 763.68 s to fill the trough

Explanation:

Flow rate,

V = Qt ... Equation 1

Where Q = flow rate, V = volume, t = time

making t the subject of equation 1

t = V/Q ... Equation 2

But,

Q = Av ... Equation 3

Where A = area, v = velocity.

Given: v = 1.5 m/s, and

A = πd²/4 where d = 2.0 cm = 0.02 m, π = 3.143

A = 3.143 (0.02) ²/4

A = 0.0003143 m³

Substituting these values into equation 3,

Q = 1.5*0.0003143 = 0.0004714 m³/s

Also, V = lbw ... Equation 4

Where l = length, b = width, w = width.

given: l = 1.5 m, b = 40 cm = 0.4 m, w = 60 cm = 0.6 m.

Substituting these values into 4,

V = 1.5*0.4*0.6

V = 0.36 m³.

using Equation 2,

t = V/Q

Where V = 0.36 cm³, Q = 0.0004714 m³/s

therefore,

t = 0.36/0.0004714

t = 763.68 s

Therefore it will take him 763.68 s to fill the trough