Question

2) 3,160 tons of water flows over Niagra Falls every second. Assuming the water has a density of 1.00 g/ml,

how much time would it take the water to fill up a cylinder with the diameter of a school garbage can (53 cm)
that stretched to the moon, which is on average 236,000 miles from the earth? Answer in a time unit that is
most meaningful (for example 1.40 days is more meaningful than 121,000 seconds). 1 ton = 2000 pounds

Answer 1

Time = 8.12 h = 0.34 day

Step-by-step explanation:

First we find speed of water flow:

Speed = u = (3160 tons/s)(907.185 kg/1 ton)

u = 2866704.6 kg/s

also,

Density = (1 g/mL)(1 mL/1 x 10⁻⁶ m³)(1 x 10⁻³ kg/1 g)

Density = 1000 kg/m³

Now,

Volume Flow Rate = Speed/Density

Volume Flow Rate = (2866704.6 kg/s)/(1000 kg/m³)

Volume Flow Rate = 2866.7 m³/s

Now, we find volume of cylinder:

Volume = (Area)(Length)

Volume = (πd²/4)(L)

Volume = [(π)(0.53 m)²/4][236000 mi][1609.36 m/1 mi]

Volume = 83,792,823.82 m³

Now,

Time = Volume/Volume Flow Rate

Time = (83,792,823.82 m³)/(2866.7 m³/s)

Time = (29299.71 s)(1 h/3600 s)

Time = 8.12 h = 0.34 day