A cowboy at a ranch fills a water trough that is 1.5 meters long, 65 cm wide and 45 cm deep. He uses a hose having a diameter of 2 cm, and the water emerges from the hose at 1.5 m/s. How long does it take the cowboy to fill the trough?
Volume to fill, V, in m³
= 1.5m * 0.65m * 0.45m
Filling rate, f, in m³/s
=π(0.01)²*1.5
Time to fill, t, in seconds
= V/f
To find out how long it takes the cowboy to fill the trough, we need to calculate the volume of the trough and then determine the flow rate of the water from the hose.
First, let's calculate the volume of the water trough:
The length of the trough is given as 1.5 meters, the width is given as 65 cm (which is 0.65 meters), and the depth is given as 45 cm (which is 0.45 meters).
The volume of a rectangular shape is calculated by multiplying together its length, width, and depth.
So, the volume of the water trough is: Volume = Length x Width x Depth = 1.5 m x 0.65 m x 0.45 m.
Next, we need to calculate the flow rate of the water from the hose:
The flow rate of a liquid is determined by the cross-sectional area of the hose and the speed of the liquid.
The area of a circular cross-section is calculated using the formula: Area = π x (radius)^2.
In this case, the diameter of the hose is given as 2 cm, which means the radius is 1 cm (or 0.01 meters).
So, the area of the hose is: Area = π x (0.01 m)^2.
Now, we can calculate the flow rate:
Flow Rate = Area x Speed = (π x (0.01 m)^2) x 1.5 m/s.
Finally, to find the time it takes to fill the trough, we divide the volume of the trough by the flow rate of the water:
Time = Volume / Flow Rate.
By substituting the values into the equation, you can find the exact time it takes the cowboy to fill the trough.