The spout heights in the container in the figure are 15 cm, 30 cm, 45 cm, and 60 cm. The water level is maintained at a 68 cm height by an outside supply.

What is the speed of the water out of the 15 cm high hole?

What is the speed of the water out of the 30 cm high hole?

What is the speed of the water out of the 45 cm high hole?

What is the speed of the water out of the 60 cm high hole?

Which water stream has the greatest range relative to the base of the container?

A. the stream from 15 cm
B. the stream from 30 cm
C. the stream from 45 cm
D. the stream from 60 cm

To find the speed of the water coming out of each hole, you can use Torricelli's law, which states that the speed (v) of a liquid flowing out of an opening is given by the equation:

v = sqrt(2gh)

Where:
- v is the speed of the water
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height of the water above the opening

Note that in this case, the height (h) is given in centimeters, so we'll need to convert it to meters by dividing by 100.

Let's calculate the speed for each hole:

1. For the 15 cm high hole:
h = 15 cm = 0.15 m
v = sqrt(2 * 9.8 * 0.15) ≈ 1.9 m/s

2. For the 30 cm high hole:
h = 30 cm = 0.30 m
v = sqrt(2 * 9.8 * 0.30) ≈ 2.7 m/s

3. For the 45 cm high hole:
h = 45 cm = 0.45 m
v = sqrt(2 * 9.8 * 0.45) ≈ 3.7 m/s

4. For the 60 cm high hole:
h = 60 cm = 0.60 m
v = sqrt(2 * 9.8 * 0.60) ≈ 4.5 m/s

Therefore, the speed of the water coming out of the 15 cm, 30 cm, 45 cm, and 60 cm holes are approximately 1.9 m/s, 2.7 m/s, 3.7 m/s, and 4.5 m/s respectively.

To determine which water stream has the greatest range, we need to calculate the horizontal distance the water will travel before hitting the ground. This can be done by using the equation:

range = v * t

Where:
- range is the horizontal distance traveled
- v is the speed of the water
- t is the time it takes for the water to hit the ground

Since all the streams start with the same initial vertical height (68 cm) and will hit the ground at the same time, we can ignore the time and focus only on the speed (v) to determine the greatest range.

The stream with the greatest speed is the one coming from the 60 cm high hole, with a speed of approximately 4.5 m/s. Therefore, the answer is D. the stream from 60 cm.