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Answer :
Let's work through each unit conversion step-by-step.
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1. Converting 60 miles per hour to meters per second:
We know that:
- 1 mile = 1609.34 meters
- 1 hour = 3600 seconds
Thus, the conversion factor is
[tex]$$
\frac{1609.34 \text{ meters}}{3600 \text{ seconds}} \approx 0.447038888888889 \, \frac{\text{m}}{\text{s per mph}}.
$$[/tex]
Therefore, for a speed of 60 mph:
[tex]$$
60 \times 0.447038888888889 \approx 26.82233 \, \text{meters per second}.
$$[/tex]
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2. Converting 200 psi (pounds per square inch) to kilograms per square centimeter:
It is given that approximately
[tex]$$
1 \, \text{psi} \approx 0.070307 \, \frac{\text{kg}}{\text{cm}^2}.
$$[/tex]
Hence, for 200 psi:
[tex]$$
200 \times 0.070307 \approx 14.0614 \, \frac{\text{kg}}{\text{cm}^2}.
$$[/tex]
--------------------------------------------------
3. Converting 1 cubic yard per minute to cubic feet per hour:
We use the facts:
- 1 cubic yard = 27 cubic feet
- 1 hour = 60 minutes
So, converting the volume:
[tex]$$
1 \, \text{cubic yard/minute} = 27 \, \text{cubic feet/minute}.
$$[/tex]
Now converting minutes to hours:
[tex]$$
27 \, \text{cubic feet/minute} \times 60 \, \text{minutes/hour} = 1620 \, \text{cubic feet/hour}.
$$[/tex]
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4. Converting 10 gallons per minute to liters per second:
Using the conversion:
- 1 gallon = 3.78541 liters
- 1 minute = 60 seconds
First, convert gallons per minute to liters per minute:
[tex]$$
10 \, \text{gallons/minute} \times 3.78541 \, \frac{\text{liters}}{\text{gallon}} \approx 37.8541 \, \text{liters/minute}.
$$[/tex]
Then convert to liters per second:
[tex]$$
\frac{37.8541 \, \text{liters/minute}}{60 \, \text{seconds/minute}} \approx 0.630901666666667 \, \text{liters/second}.
$$[/tex]
--------------------------------------------------
In summary, the answers are:
1. Speed: approximately [tex]$26.82233$[/tex] meters per second.
2. Pressure: approximately [tex]$14.0614$[/tex] kilograms per square centimeter.
3. Rate: [tex]$1620$[/tex] cubic feet per hour.
4. Water flow: approximately [tex]$0.63090$[/tex] liters per second.
--------------------------------------------------
1. Converting 60 miles per hour to meters per second:
We know that:
- 1 mile = 1609.34 meters
- 1 hour = 3600 seconds
Thus, the conversion factor is
[tex]$$
\frac{1609.34 \text{ meters}}{3600 \text{ seconds}} \approx 0.447038888888889 \, \frac{\text{m}}{\text{s per mph}}.
$$[/tex]
Therefore, for a speed of 60 mph:
[tex]$$
60 \times 0.447038888888889 \approx 26.82233 \, \text{meters per second}.
$$[/tex]
--------------------------------------------------
2. Converting 200 psi (pounds per square inch) to kilograms per square centimeter:
It is given that approximately
[tex]$$
1 \, \text{psi} \approx 0.070307 \, \frac{\text{kg}}{\text{cm}^2}.
$$[/tex]
Hence, for 200 psi:
[tex]$$
200 \times 0.070307 \approx 14.0614 \, \frac{\text{kg}}{\text{cm}^2}.
$$[/tex]
--------------------------------------------------
3. Converting 1 cubic yard per minute to cubic feet per hour:
We use the facts:
- 1 cubic yard = 27 cubic feet
- 1 hour = 60 minutes
So, converting the volume:
[tex]$$
1 \, \text{cubic yard/minute} = 27 \, \text{cubic feet/minute}.
$$[/tex]
Now converting minutes to hours:
[tex]$$
27 \, \text{cubic feet/minute} \times 60 \, \text{minutes/hour} = 1620 \, \text{cubic feet/hour}.
$$[/tex]
--------------------------------------------------
4. Converting 10 gallons per minute to liters per second:
Using the conversion:
- 1 gallon = 3.78541 liters
- 1 minute = 60 seconds
First, convert gallons per minute to liters per minute:
[tex]$$
10 \, \text{gallons/minute} \times 3.78541 \, \frac{\text{liters}}{\text{gallon}} \approx 37.8541 \, \text{liters/minute}.
$$[/tex]
Then convert to liters per second:
[tex]$$
\frac{37.8541 \, \text{liters/minute}}{60 \, \text{seconds/minute}} \approx 0.630901666666667 \, \text{liters/second}.
$$[/tex]
--------------------------------------------------
In summary, the answers are:
1. Speed: approximately [tex]$26.82233$[/tex] meters per second.
2. Pressure: approximately [tex]$14.0614$[/tex] kilograms per square centimeter.
3. Rate: [tex]$1620$[/tex] cubic feet per hour.
4. Water flow: approximately [tex]$0.63090$[/tex] liters per second.
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