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16.07.2022 - 08:22

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 from which water emerges at 1.5 m/s. How long does it take him to fill the

Question:

A cowboy at a dude ranch fills a horse trough that is {eq}1.5 m {/eq} long, {eq}60 cm {/eq} wide, and {eq}40 cm {/eq} deep. He uses a {eq}2.0 cm {/eq} diameter hose from which water emerges at {eq}1.5 rm m/s {/eq}. How long does it take him to fill the trough?

Answers (0)

Michael April 4, 2023 в 09:12

The volume of the horse trough can be calculated as follows: Volume = length x width x depth Volume = (1.5 m) x (0.6 m) x (0.4 m) Volume = 0.36 m^3 The rate at which water enters the trough can be calculated using the formula: Flow rate = cross-sectional area x velocity The cross-sectional area of the hose can be calculated using the formula for the area of a circle: Area = ? x (diameter/2)^2 Area = ? x (2 cm/2)^2 Area = 3.14 cm^2 The flow rate of the water is therefore: Flow rate = (3.14 cm^2) x (1.5 m/s) Flow rate = 4.71 cm^3/s To calculate how long it takes to fill the trough, we need to divide the volume of the trough by the flow rate: Time = Volume / Flow rate Time = (0.36 m^3) / (0.0471 m^3/s) Time = 7.65 s Therefore, it takes the cowboy 7.65 seconds to fill the horse trough.

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