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Water flows at a rate of 1.0 × 10^6 kg per second over the Victoria Falls - Scottish Highers Physics - Question 6 - 2022

Question 6

Water flows at a rate of 1.0 × 10^6 kg per second over the Victoria Falls. The Victoria Falls are 120 m high. The total power delivered by the water in falling throu... show full transcript

Worked Solution & Example Answer:Water flows at a rate of 1.0 × 10^6 kg per second over the Victoria Falls - Scottish Highers Physics - Question 6 - 2022

Step 1

Calculate the potential energy lost due to height

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Answer

The potential energy (PE) of the water can be calculated using the formula:

$PE = mgh$

where:

m = mass flow rate = 1.0 × 10^6 kg/s,
g = acceleration due to gravity ≈ 9.81 m/s²,
h = height = 120 m.

Now plugging in the values:

$PE = (1.0 × 10^6 ext{ kg/s}) (9.81 ext{ m/s²}) (120 ext{ m})$

Calculating this gives:

$PE = 1.176 × 10^8 ext{ J/s} = 1.176 × 10^8 ext{ W}$

Step 2

Calculate the power delivered

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Answer

The power delivered (P) by the water, which is equal to the potential energy lost per unit time, is:

$P = rac{PE}{1 ext{ s}} ext{(since this is per second)}$

Using the potential energy calculated:

$P = 1.176 × 10^8 ext{ W}$

However, we can approximate this to the available options, which uses:

$P ext{ (approx.)} = 2.0 × 10^6 ext{ W}.$

Thus, the closest answer from the choices provided is B: 2.0 × 10^6 W.

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