A cowboy at a dude ranch fills a horse trough that is 1.53 m long, 61 cm wide, and 42 cm deep. He uses a 2.0-cm-diameter hose from which water emerges at 1.66 m/s. How long does it take him to fill the trough?

It takes him 751.39 seconds to fill the trough

Explanation:

The flow rate = Velocity of the hose * cross sectional area of the hose.

Q = V*A ... Equation 1

Where Q = flow rate, V = velocity, A = cross sectional area.

Given: V = 1.66 m/s,

A = πd²/4, Where d = 2.00 cm = 0.02 m.

Therefore, A = 3.143 (0.02) ²/4 = 0.0003143 m²

Substituting these values into equation 1

Q = 1.66*0.0003143

Q = 0.0005217 m³/s.

Time taken to fill the trough = Volume of the trough/flow rate.

t = V/Q ... Equation 2.

Where V = volume of the trough, Q = flow rate.

Given: Q = 0.0005217 m³/s, V = length*width*height = l*w*h, l = 1.53 m, w = 61 cm = 0.61 m, h = 42 cm = 0.42 m.

V = 1.53*0.61*0.42 = 0.392 cm³

Substituting these value into equation 2,

t = 0.392/0.0005217

t = 751.39 seconds.

Thus it takes him 751.39 seconds to fill the trough