Answer :
Sure, let's go through the steps to solve the given questions:
1. Convert the units of speeds from km/h to m/s:
To convert km/h to m/s, we use the conversion factor: [tex]\( \frac{1000 \text{ meters}}{3600 \text{ seconds}} = \frac{5}{18} \)[/tex].
a. 72 km/h to m/s:
[tex]\[
72 \times \frac{5}{18} = 20 \text{ m/s}
\][/tex]
b. 108 km/h to m/s:
[tex]\[
108 \times \frac{5}{18} = 30 \text{ m/s}
\][/tex]
c. 900 km/h to m/s:
[tex]\[
900 \times \frac{5}{18} = 250 \text{ m/s}
\][/tex]
2. Convert the units of speeds from m/s to km/h:
To convert m/s to km/h, we use the conversion factor: [tex]\( \frac{3600 \text{ seconds}}{1000 \text{ meters}} = \frac{18}{5} \)[/tex].
a. 25 m/s to km/h:
[tex]\[
25 \times \frac{18}{5} = 90 \text{ km/h}
\][/tex]
b. 45 m/s to km/h:
[tex]\[
45 \times \frac{18}{5} = 162 \text{ km/h}
\][/tex]
c. 15 m/s to km/h:
[tex]\[
15 \times \frac{18}{5} = 54 \text{ km/h}
\][/tex]
3. An aeroplane traveling at 625 km/h:
a. Time taken to reach a city 1250 km away:
Time is calculated by dividing the distance by speed:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{1250}{625} = 2 \text{ hours}
\][/tex]
b. Distance covered in 45 minutes:
First, convert 45 minutes to hours:
[tex]\[
\text{Time in hours} = \frac{45}{60} = 0.75 \text{ hours}
\][/tex]
Then, calculate the distance:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time} = 625 \times 0.75 = 468.75 \text{ km}
\][/tex]
c. Distance covered in 15 seconds:
First, convert 15 seconds to hours:
[tex]\[
\text{Time in hours} = \frac{15}{3600} \approx 0.004167 \text{ hours}
\][/tex]
Then, calculate the distance:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time} = 625 \times 0.004167 \approx 2.604 \text{ km}
\][/tex]
If you have any more questions or need further clarification, feel free to ask!
1. Convert the units of speeds from km/h to m/s:
To convert km/h to m/s, we use the conversion factor: [tex]\( \frac{1000 \text{ meters}}{3600 \text{ seconds}} = \frac{5}{18} \)[/tex].
a. 72 km/h to m/s:
[tex]\[
72 \times \frac{5}{18} = 20 \text{ m/s}
\][/tex]
b. 108 km/h to m/s:
[tex]\[
108 \times \frac{5}{18} = 30 \text{ m/s}
\][/tex]
c. 900 km/h to m/s:
[tex]\[
900 \times \frac{5}{18} = 250 \text{ m/s}
\][/tex]
2. Convert the units of speeds from m/s to km/h:
To convert m/s to km/h, we use the conversion factor: [tex]\( \frac{3600 \text{ seconds}}{1000 \text{ meters}} = \frac{18}{5} \)[/tex].
a. 25 m/s to km/h:
[tex]\[
25 \times \frac{18}{5} = 90 \text{ km/h}
\][/tex]
b. 45 m/s to km/h:
[tex]\[
45 \times \frac{18}{5} = 162 \text{ km/h}
\][/tex]
c. 15 m/s to km/h:
[tex]\[
15 \times \frac{18}{5} = 54 \text{ km/h}
\][/tex]
3. An aeroplane traveling at 625 km/h:
a. Time taken to reach a city 1250 km away:
Time is calculated by dividing the distance by speed:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{1250}{625} = 2 \text{ hours}
\][/tex]
b. Distance covered in 45 minutes:
First, convert 45 minutes to hours:
[tex]\[
\text{Time in hours} = \frac{45}{60} = 0.75 \text{ hours}
\][/tex]
Then, calculate the distance:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time} = 625 \times 0.75 = 468.75 \text{ km}
\][/tex]
c. Distance covered in 15 seconds:
First, convert 15 seconds to hours:
[tex]\[
\text{Time in hours} = \frac{15}{3600} \approx 0.004167 \text{ hours}
\][/tex]
Then, calculate the distance:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time} = 625 \times 0.004167 \approx 2.604 \text{ km}
\][/tex]
If you have any more questions or need further clarification, feel free to ask!
