A cowboy at a dude ranch fills a horse trough that is 1.7 m long, 50 cm wide, and 40 cm deep. He uses a 1.9 cm diameter hose from which water emerges at 1.3 m/s. How long does it take him to fill the trough?
min
To find the time it takes to fill the trough, we need to calculate the volume of the trough and then determine how long it takes for the water to fill that volume.
First, let's convert the measurements to meters:
- Length: 1.7 m
- Width: 0.50 m (50 cm = 0.50 m)
- Depth: 0.40 m (40 cm = 0.40 m)
To find the volume of the trough, we multiply the length, width, and depth:
Volume = Length x Width x Depth
Volume = 1.7 m x 0.50 m x 0.40 m
Volume = 0.34 m³
Now, let's calculate how long it takes for the water to fill this volume. We'll need to know the cross-sectional area of the hose, as well as the velocity at which the water is flowing.
The cross-sectional area of the hose can be found using the formula:
Area = π x (radius)²
where radius = diameter/2.
Given that the diameter of the hose is 1.9 cm = 0.019 m, we can calculate the radius:
radius = 0.019 m / 2
radius = 0.0095 m
Now, let's calculate the area:
Area = π x (0.0095 m)²
Area ≈ 0.000283 m²
To find the time it takes to fill the trough, we'll use the equation:
Time = Volume / Flow rate
Given that the flow rate is 1.3 m/s and the volume is 0.34 m³, we can calculate the time:
Time = 0.34 m³ / 1.3 m/s
Time ≈ 0.26 s
Therefore, it takes approximately 0.26 seconds for the cowboy to fill the trough.
(Volume of trough)/(Volume flow rate of water)
= (w*l*d)/(pi*r^2*v)
w, l, d, r, v = width, length, depth, radius and velocity respectively
Use the same length units for all terms (cm or meters) to get the answer in seconds