High School

1. Convert the following speeds into [tex]m/s[/tex]:

a. [tex]72 \, km/h[/tex]

b. [tex]108 \, km/h[/tex]

c. [tex]900 \, km/h[/tex]

2. Convert the following speeds into [tex]km/h[/tex]:

a. [tex]25 \, m/s[/tex]

b. [tex]45 \, m/s[/tex]

c. [tex]15 \, m/s[/tex]

3. An airplane is flying at a speed of [tex]625 \, km/h[/tex].

a. If the distance between two cities is [tex]1250 \, km[/tex], find the time taken to reach the destination by the airplane.

b. How much distance is covered in 45 minutes?

c. How much distance is covered in 15 seconds?

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!